Complex.Atan(Complex) Method

Definition

Namespace:

System.Numerics

Assembly:

System.Runtime.Numerics.dll

Source:

Complex.cs

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

Complex

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))

See also

• Tan(Complex)
• Atan(Double)