# Complex.Reciprocal Method

.NET Framework 4

Returns the multiplicative inverse of a complex number.

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

## Syntax

```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.

## Remarks

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.

## Examples

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)

```

Supported in: 4

Supported in: 4

## Platforms

Windows 7, Windows Vista SP1 or later, Windows XP SP3, Windows Server 2008 (Server Core not supported), Windows Server 2008 R2 (Server Core supported with SP1 or later), Windows Server 2003 SP2

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