# Complex.Atan(Complex) Method

## Definition

Returns the angle that is the arc tangent of the specified complex number.

``````public:
static System::Numerics::Complex Atan(System::Numerics::Complex value);``````
``public static System.Numerics.Complex Atan (System.Numerics.Complex value);``
``static member Atan : System.Numerics.Complex -> System.Numerics.Complex``
``Public Shared Function Atan (value As Complex) As Complex``

#### Parameters

value
Complex

A complex number.

#### Returns

The angle that is the arc tangent of `value`.

## Examples

The following example illustrates the Atan method. It shows that passing the value returned by the Atan method to the Tan method returns the original Complex value.

``````using System;
using System.Numerics;

public class Example
{
public static void Main()
{
Complex[] values = { new Complex(2.5, 1.5),
new Complex(2.5, -1.5),
new Complex(-2.5, 1.5),
new Complex(-2.5, -1.5) };
foreach (Complex value in values)
Console.WriteLine("Tan(Atan({0})) = {1}",
value, Complex.Tan(Complex.Atan(value)));
}
}
// The example displays the following output:
//       Tan(Atan((2.5, 1.5))) = (2.5, 1.5)
//       Tan(Atan((2.5, -1.5))) = (2.5, -1.5)
//       Tan(Atan((-2.5, 1.5))) = (-2.5, 1.5)
//       Tan(Atan((-2.5, -1.5))) = (-2.5, -1.5)
``````
``````Imports System.Numerics

Module Example
Public Sub Main()
Dim values() As Complex = { New Complex(2.5, 1.5),
New Complex(2.5, -1.5),
New Complex(-2.5, 1.5),
New Complex(-2.5, -1.5) }
For Each value As Complex In values
Console.WriteLine("Tan(Atan({0})) = {1}",
value, Complex.Tan(Complex.Atan(value)))
Next
End Sub
End Module
' The example displays the following example:
'       Tan(Atan((2.5, 1.5))) = (2.5, 1.5)
'       Tan(Atan((2.5, -1.5))) = (2.5, -1.5)
'       Tan(Atan((-2.5, 1.5))) = (-2.5, 1.5)
'       Tan(Atan((-2.5, -1.5))) = (-2.5, -1.5)
``````

## Remarks

The Atan method for complex numbers corresponds to the Math.Atan method for real numbers.

The Atan method uses the following formula:

(ImaginaryOne / new Complex(2.0, 0.0)) * (Log(One - ImaginaryOne * value) - Log(One + ImaginaryOne * value))