# Complex.Reciprocal Method (Complex)

.NET Framework (current version)

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)
```

## Version Information

Universal Windows Platform
Available since 8
.NET Framework
Available since 4.0
Portable Class Library
Supported in: portable .NET platforms
Silverlight
Available since 4.0
Windows Phone
Available since 8.1