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Complex.Reciprocal Method

Returns the multiplicative inverse of a complex number.

Namespace:  System.Numerics
Assembly:  System.Numerics (in System.Numerics.dll)

public static Complex Reciprocal(
	Complex value
)

Parameters

value
Type: System.Numerics.Complex

A complex number.

Return Value

Type: System.Numerics.Complex
The reciprocal of value.

The reciprocal, or multiplicative inverse, of a number x is a number y where x multiplied by y yields 1. The reciprocal of a complex number is the complex number that produces Complex.One when the two numbers are multiplied. If a complex number is represented by a +bi, its reciprocal is represented by the expression a/(a2+b2) + -b/(a2 + b2).

If value is Complex.Zero, the method returns Complex.Zero. Otherwise, it returns the result of the expression Complex.One/value.

The following example uses the Reciprocal method to calculate the reciprocal values of several complex numbers. It also demonstrates that the result of multiplying a complex number by its reciprocal is Complex.One.

using System;
using System.Numerics;

public class Example
{
   public static void Main()
   {
      Complex[] values = { new Complex(1, 1), 
                           new Complex(-1, 1), 
                           new Complex(10, -1),
                           new Complex(3, 5) };
      foreach (Complex value in values)
      {         
         Complex r1 = Complex.Reciprocal(value);                   
         Console.WriteLine("{0:N0} x {1:N2} = {2:N2}", 
                           value, r1, value * r1);
      }
   }
}
// The example displays the following output: 
//       (1, 1) x (0.50, -0.50) = (1.00, 0.00) 
//       (-1, 1) x (-0.50, -0.50) = (1.00, 0.00) 
//       (10, -1) x (0.10, 0.01) = (1.00, 0.00) 
//       (3, 5) x (0.09, -0.15) = (1.00, 0.00)

.NET Framework

Supported in: 4.5, 4

.NET Framework Client Profile

Supported in: 4

Portable Class Library

Supported in: Portable Class Library

.NET for Windows Store apps

Supported in: Windows 8

.NET for Windows Phone apps

Supported in: Windows Phone 8.1

Windows Phone 8.1, Windows 8.1, Windows Server 2012 R2, Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

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