# Complex.FromPolarCoordinates(Double, Double) Method

## Definition

Creates a complex number from a point's polar coordinates.

``````public:
static System::Numerics::Complex FromPolarCoordinates(double magnitude, double phase);``````
``public static System.Numerics.Complex FromPolarCoordinates (double magnitude, double phase);``
``static member FromPolarCoordinates : double * double -> System.Numerics.Complex``
``Public Shared Function FromPolarCoordinates (magnitude As Double, phase As Double) As Complex``

#### Parameters

magnitude
Double

The magnitude, which is the distance from the origin (the intersection of the x-axis and the y-axis) to the number.

phase
Double

The phase, which is the angle from the line to the horizontal axis, measured in radians.

#### Returns

Complex

A complex number.

## Examples

The following example uses the FromPolarCoordinates method to instantiate a complex number based on its polar coordinates and then displays the value of its Magnitude and Phase properties.

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

public class Example
{
public static void Main()
{
Complex c1 = Complex.FromPolarCoordinates(10, 45 * Math.PI / 180);
Console.WriteLine("{0}:", c1);
Console.WriteLine("   Magnitude: {0}", Complex.Abs(c1));
Console.WriteLine("   Phase      {0} degrees", c1.Phase * 180/Math.PI);
Console.WriteLine("   Atan(b/a): {0}", Math.Atan(c1.Imaginary/c1.Real));
}
}
// The example displays the following output:
//       (7.07106781186548, 7.07106781186547):
//          Magnitude: 10
//          Phase      45 degrees
//          Atan(b/a): 0.785398163397448
``````
``````Imports System.Numerics

Module Example
Public Sub Main()
Dim c1 As Complex = Complex.FromPolarCoordinates(10, 45 * Math.Pi / 180)
Console.WriteLine("{0}:", c1)
Console.WriteLine("   Magnitude: {0}", Complex.Abs(c1))
Console.WriteLine("   Phase      {0} degrees", c1.Phase * 180/Math.Pi)
Console.WriteLine("   Atan(b/a): {0}", Math.Atan(c1.Imaginary/c1.Real))
End Sub
End Module
' The example displays the following output:
'       (7.07106781186548, 7.07106781186547):
'          Magnitude: 10
'          Phase      45 degrees
'          Atan(b/a): 0.785398163397448
``````

## Remarks

The FromPolarCoordinates method instantiates a complex number based on its polar coordinates.

Because there are multiple representations of a point on a complex plane, the return value of the FromPolarCoordinates method is normalized. The magnitude is normalized to a positive number, and the phase is normalized to a value in the range of -PI to PI. As a result, the values of the Phase and Magnitude properties of the resulting complex number may not equal the original values of the `magnitude` and `phase` parameters.

To convert a value from degrees to radians for the `phase` parameter, multiply it by Math.PI/180.