Complex.FromPolarCoordinates(Double, Double) Method

Definition

Namespace:

System.Numerics

Assemblies:

netstandard.dll, System.Runtime.Numerics.dll

Source:

Complex.cs

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

C#

public static System.Numerics.Complex FromPolarCoordinates(double magnitude, double phase);

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.

C#

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} radians", c1.Phase);
      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:     0.785398163397448 radians
//          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 might 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 $\frac{\pi }{180}$.

Applies to

See also

• Magnitude
• Phase