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Added documentation for System.Numerics.Complex APIs targeted for 3.0 (#2946)
* Adding documentation for System.Numerics APIs. * Fixing typo missed in #2912 * Fixing syntax errors.
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‎xml/System.Numerics/Complex.xml‎

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@@ -314,6 +314,31 @@
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<altmember cref="M:System.Math.Acos(System.Double)" />
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</Docs>
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</Member>
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<MemberGroup MemberName="Add">
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<Docs>
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<summary>Adds a specified number to another specified number, where at least one of them is a complex number, and the other could be a double-precision real number.</summary>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The <xref:System.Numerics.Complex.Add%2A> methods allow performing addition operations that involve complex numbers.
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If the method call results in an overflow in either the real or imaginary component, the value of the component is either <xref:System.Double.PositiveInfinity?displayProperty=nameWithType> or <xref:System.Double.NegativeInfinity?displayProperty=nameWithType>.
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Languages that do not support custom operators can use the <xref:System.Numerics.Complex.Add%2A> method to perform addition with complex numbers.
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The <xref:System.Numerics.Complex.Add%2A> methods that receive one double are more efficient than the methods that receive two complex numbers.
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## Examples
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The following example illustrates addition with complex numbers.
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[!code-csharp[System.Numerics.Complex.Add#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add1.cs#1)]
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[!code-vb[System.Numerics.Complex.Add#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add1.vb#1)]
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]]></format>
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</remarks>
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</Docs>
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</MemberGroup>
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<Member MemberName="Add">
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<MemberSignature Language="C#" Value="public static System.Numerics.Complex Add (double left, System.Numerics.Complex right);" />
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<MemberSignature Language="ILAsm" Value=".method public static hidebysig valuetype System.Numerics.Complex Add(float64 left, valuetype System.Numerics.Complex right) cil managed" />
@@ -340,11 +365,19 @@
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<Parameter Name="right" Type="System.Numerics.Complex" Index="1" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="left">To be added.</param>
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<param name="right">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<remarks>To be added.</remarks>
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<param name="left">The double-precision real value to add.</param>
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<param name="right">The complex value to add.</param>
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<summary>Adds a double-precision real number to a complex number and returns the result.</summary>
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<returns>The sum of <paramref name="left" /> and <paramref name="right" />.</returns>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The addition of a real number (which can be regarded as the complex number a + 0i) and a complex number (c + di) takes the following form:
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(a + c) + di
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Addition(System.Double,System.Numerics.Complex)" />
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</Docs>
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</Member>
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<Member MemberName="Add">
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<Parameter Name="right" Type="System.Double" Index="1" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="left">To be added.</param>
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<param name="right">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<remarks>To be added.</remarks>
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<param name="left">The complex value to add.</param>
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<param name="right">The double-precision real value to add.</param>
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<summary>Adds a complex number to a double-precision real number and returns the result.</summary>
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<returns>The sum of <paramref name="left" /> and <paramref name="right" />.</returns>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The addition of a complex number (a + bi) and a real number (which can be regarded as the complex number c + 0i) takes the following form:
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(a + c) + bi
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Addition(System.Numerics.Complex,System.Double)" />
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</Docs>
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</Member>
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<Member MemberName="Add">
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The addition of a complex number, a + bi, and a second complex number, c + di, takes the following form:
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(a + c) + (b + d)i.
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If the method call results in an overflow in either the real or imaginary component, the value of the component is either <xref:System.Double.PositiveInfinity?displayProperty=nameWithType> or <xref:System.Double.NegativeInfinity?displayProperty=nameWithType>.
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Languages that do not support custom operators can use the <xref:System.Numerics.Complex.Add%2A> method to perform addition with complex numbers.
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## Examples
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The following example illustrates addition with complex numbers.
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[!code-csharp[System.Numerics.Complex.Add#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add1.cs#1)]
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[!code-vb[System.Numerics.Complex.Add#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add1.vb#1)]
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]]></format>
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</remarks>
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<altmember cref="M:System.Math.Cosh(System.Double)" />
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</Docs>
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</Member>
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<MemberGroup MemberName="Divide">
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<Docs>
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<summary>Divides a specified number by another specified number, where at least one of them is a complex number, and the other could be a double-precision real number.</summary>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The <xref:System.Numerics.Complex.Divide%2A> methods allow performing division operations that involve complex numbers.
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If the calculation of the quotient results in an overflow in either the real or imaginary component, the value of that component is either <xref:System.Double.PositiveInfinity?displayProperty=nameWithType> or <xref:System.Double.NegativeInfinity?displayProperty=nameWithType>.
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The <xref:System.Numerics.Complex.Divide%2A> method can be used by languages that do not support custom operators. Its behavior is identical to division using the division operator.
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The <xref:System.Numerics.Complex.Divide%2A> methods that receive one double are more efficient than the methods that receive two complex numbers.
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## Examples
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The following example divides a complex number by each element in an array of complex numbers.
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[!code-csharp[System.Numerics.Complex.Divide#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.divide/cs/divide1.cs#1)]
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[!code-vb[System.Numerics.Complex.Divide#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.divide/vb/divide1.vb#1)]
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]]></format>
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</remarks>
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</Docs>
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</MemberGroup>
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<Member MemberName="Divide">
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<MemberSignature Language="C#" Value="public static System.Numerics.Complex Divide (double dividend, System.Numerics.Complex divisor);" />
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<MemberSignature Language="ILAsm" Value=".method public static hidebysig valuetype System.Numerics.Complex Divide(float64 dividend, valuetype System.Numerics.Complex divisor) cil managed" />
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<Parameter Name="divisor" Type="System.Numerics.Complex" Index="1" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="dividend">To be added.</param>
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<param name="divisor">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<remarks>To be added.</remarks>
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<param name="dividend">The double-precision real number to be divided.</param>
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<param name="divisor">The complex number to divide by.</param>
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<summary>Divides one double-precision real number by a complex number and returns the result.</summary>
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<returns>The quotient of the division.</returns>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The division of a real number (which can be regarded as the complex number a + 0i) and a complex number (c + di) takes the following form:
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(ac / (c<sup>2</sup> + d<sup>2</sup>)) + (ad / (c<sup>2</sup> + d<sup>2</sup>)i
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Division(System.Double,System.Numerics.Complex)" />
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</Docs>
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</Member>
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<Member MemberName="Divide">
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<Parameter Name="divisor" Type="System.Double" Index="1" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="dividend">To be added.</param>
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<param name="divisor">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<remarks>To be added.</remarks>
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<param name="dividend">The complex number to be divided.</param>
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<param name="divisor">The double-precision real number to divide by.</param>
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<summary>Divides one complex number by a double-precision real number and returns the result.</summary>
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<returns>The quotient of the division.</returns>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The division of a complex number (a + bi) and a real number (which can be regarded as the complex number c + 0i) takes the following form:
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(ac / c<sup>2</sup>) + (bc / c<sup>2</sup>)i
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Division(System.Numerics.Complex,System.Double)" />
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</Docs>
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</Member>
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<Member MemberName="Divide">
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The division of a complex number, a + bi, by a second complex number, number, c + di, takes the following form:
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((ac + bd) / (c<sup>2</sup> + d<sup>2</sup>)) + ((bc - ad) / (c<sup>2</sup> + d<sup>2</sup>)i
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If the calculation of the quotient results in an overflow in either the real or imaginary component, the value of that component is either <xref:System.Double.PositiveInfinity?displayProperty=nameWithType> or <xref:System.Double.NegativeInfinity?displayProperty=nameWithType>.
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The <xref:System.Numerics.Complex.Divide%2A> method can be used by languages that do not support custom operators. Its behavior is identical to division using the division operator.
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## Examples
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The following example divides a complex number by each element in an array of complex numbers.
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[!code-csharp[System.Numerics.Complex.Divide#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.divide/cs/divide1.cs#1)]
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[!code-vb[System.Numerics.Complex.Divide#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.divide/vb/divide1.vb#1)]
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Division(System.Numerics.Complex,System.Numerics.Complex)" />
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<ReturnType>System.Numerics.Complex</ReturnType>
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</ReturnValue>
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<Docs>
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<summary>To be added.</summary>
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<summary>Represents infinity as a complex number.</summary>
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<remarks>To be added.</remarks>
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</Docs>
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</Member>
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<Parameter Name="value" Type="System.Numerics.Complex" Index="0" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="value">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<param name="value">A complex number.</param>
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<summary>Determines whether the specified complex number is finite.</summary>
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<returns><see langword="true" /> if both, the real and imaginary parts are finite (zero, subnormal or normal); otherwise, <see langword="false" />.</returns>
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<remarks>To be added.</remarks>
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</Docs>
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</Member>
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<Parameter Name="value" Type="System.Numerics.Complex" Index="0" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="value">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<param name="value">A complex number.</param>
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<summary>Returns a value indicating whether the specified complex number evaluates to infinity.</summary>
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<returns><see langword="true"/> if either, the real or imaginary part are <see cref="F:System.Double.PositiveInfinity" /> or <see cref="F:System.Double.NegativeInfinity" />; otherwise, <see langword="false"/>.</returns>
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<remarks>To be added.</remarks>
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</Docs>
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</Member>
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<Parameter Name="value" Type="System.Numerics.Complex" Index="0" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="value">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<param name="value">A complex number.</param>
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<summary>Returns a value that indicates whether the specified complex instance is not a number (NaN).</summary>
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<returns><see langword="true"/> if the specified value is not finite nor infinite; otherwise, <see langword="false"/>.</returns>
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<remarks>To be added.</remarks>
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</Docs>
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</Member>
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<altmember cref="P:System.Numerics.Complex.Phase" />
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</Docs>
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</Member>
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<MemberGroup MemberName="op_Multiply">
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<Docs>
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<summary>Multiplies a specified number by another specified number, where at least one of them is a complex number, and the other could be a double-precision real number.</summary>
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<remarks>
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<format type="text/markdown">
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<![CDATA[
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## Remarks
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The <xref:System.Numerics.Complex.Multiply%2A> methods allow performing multiplication operations that involve complex numbers.
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If the multiplication results in an overflow in either the real or imaginary component, the value of that component is either <xref:System.Double.PositiveInfinity?displayProperty=nameWithType> or <xref:System.Double.NegativeInfinity?displayProperty=nameWithType>.
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The <xref:System.Numerics.Complex.Multiply%2A> method is implemented for languages that do not support custom operators. Its behavior is identical to multiplication using the multiplication operator.
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## Examples
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The following example multiples a complex number by each element in an array of complex numbers.
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[!code-csharp[System.Numerics.Complex.Multiply#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.multiply/cs/multiply1.cs#1)]
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[!code-vb[System.Numerics.Complex.Multiply#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.multiply/vb/multiply1.vb#1)]
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]]></format>
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</remarks>
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</Docs>
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</MemberGroup>
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<Member MemberName="Multiply">
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<MemberSignature Language="C#" Value="public static System.Numerics.Complex Multiply (double left, System.Numerics.Complex right);" />
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<MemberSignature Language="ILAsm" Value=".method public static hidebysig valuetype System.Numerics.Complex Multiply(float64 left, valuetype System.Numerics.Complex right) cil managed" />
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<Parameter Name="right" Type="System.Numerics.Complex" Index="1" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="left">To be added.</param>
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<param name="right">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<remarks>To be added.</remarks>
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<param name="left">The double-precision real number to multiply.</param>
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<param name="right">The complex number to multiply.</param>
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<summary>Returns the product of a double-precision real number and a complex number.</summary>
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<returns>The product of the <paramref name="left" /> and <paramref name="right" /> parameters.</returns>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The multiplication of a real number (which can be regarded as the complex number a + 0i) and a complex number (c + di) takes the following form:
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ac + adi
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Multiply(System.Double,System.Numerics.Complex)" />
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</Docs>
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</Member>
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<Member MemberName="Multiply">
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<Parameter Name="right" Type="System.Double" Index="1" FrameworkAlternate="netcore-3.0" />
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</Parameters>
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<Docs>
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<param name="left">To be added.</param>
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<param name="right">To be added.</param>
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<summary>To be added.</summary>
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<returns>To be added.</returns>
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<remarks>To be added.</remarks>
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<param name="left">The complex number to multiply.</param>
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<param name="right">The double-precision real number to multiply.</param>
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<summary>Returns the product of a complex number and a double-precision real number.</summary>
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<returns>The product of the <paramref name="left" /> and <paramref name="right" /> parameters.</returns>
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<remarks>
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<format type="text/markdown"><![CDATA[
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## Remarks
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The multiplication of a complex number (a + bi) and a real number (which can be regarded as the complex number c + 0i) takes the following form:
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ac + bci
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Multiply(System.Numerics.Complex,System.Double)" />
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</Docs>
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</Member>
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<Member MemberName="Multiply">
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(ac - bd) + (ad + bc)i
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If the multiplication results in an overflow in either the real or imaginary component, the value of that component is either <xref:System.Double.PositiveInfinity?displayProperty=nameWithType> or <xref:System.Double.NegativeInfinity?displayProperty=nameWithType>.
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The <xref:System.Numerics.Complex.Multiply%2A> method is implemented for languages that do not support custom operators. Its behavior is identical to multiplication using the multiplication operator.
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## Examples
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The following example multiples a complex number by each element in an array of complex numbers.
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[!code-csharp[System.Numerics.Complex.Multiply#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.multiply/cs/multiply1.cs#1)]
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[!code-vb[System.Numerics.Complex.Multiply#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.multiply/vb/multiply1.vb#1)]
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.op_Multiply(System.Numerics.Complex,System.Numerics.Complex)" />
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<ReturnType>System.Numerics.Complex</ReturnType>
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</ReturnValue>
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<Docs>
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<summary>To be added.</summary>
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<summary>Represents a complex instance that is not a number (NaN).</summary>
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<remarks>To be added.</remarks>
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</Docs>
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</Member>
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]]></format>
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</remarks>
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<altmember cref="M:System.Numerics.Complex.Add(System.NDouble,System.Numerics.Complex)" />
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<altmember cref="M:System.Numerics.Complex.Add(System.Double,System.Numerics.Complex)" />
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</Docs>
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</Member>
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<Member MemberName="op_Addition">

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