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# Complex.Reciprocal Method

Visual Studio 2010

Returns the multiplicative inverse of a complex number.

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

## Syntax

```'Declaration
Public Shared Function Reciprocal ( _
value As Complex _
) As Complex
```

#### 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.

```
Imports System.Numerics

Module Example
Public Sub Main()
Dim values() As Complex = { New Complex(1, 1),
New Complex(-1, 1),
New Complex(10, -1),
New Complex(3, 5) }
For Each value As Complex In values
Dim r1 As Complex = Complex.Reciprocal(value)
Console.WriteLine("{0:N0} x {1:N2} = {2:N2}",
value, r1, value * r1)
Next
End Sub
End Module
' 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.