Complex.Abs(Complex) Method

Definition

Namespace:

System.Numerics

Assembly:

System.Runtime.Numerics.dll

Source:

Complex.cs

Gets the absolute value (or magnitude) of a complex number.

public:
 static double Abs(System::Numerics::Complex value);

public static double Abs (System.Numerics.Complex value);

static member Abs : System.Numerics.Complex -> double

Public Shared Function Abs (value As Complex) As Double

Parameters

value

Complex

A complex number.

Returns

Double

The absolute value of value.

Examples

The following example calculates the absolute value of a complex number and demonstrates that it is equivalent to the value of the Magnitude property.

using System;
using System.Numerics;

public class Example
{
   public static void Main()
   {
      Complex complex1 = new Complex(2.0, 3.0);
      Console.WriteLine("|{0}| = {1:N2}", complex1, Complex.Abs(complex1));
      Console.WriteLine("Equal to Magnitude: {0}",
                        Complex.Abs(complex1).Equals(complex1.Magnitude));
   }
}
// The example displays the following output:
//       |(2, 3)| = 3.61
//       Equal to Magnitude: True

open System.Numerics

let complex1 = Complex(2., 3.)
printfn $"|{complex1}| = {Complex.Abs complex1:N2}"
printfn $"Equal to Magnitude: {Complex.Abs(complex1).Equals complex1.Magnitude}"
// The example displays the following output:
//       |(2, 3)| = 3.61
//       Equal to Magnitude: True

Remarks

The absolute value of a complex number is equivalent to its Magnitude property. The absolute value of a complex number a + bi is calculated as follows:

• If b = 0, the result is a.
• If a > b, the result is $a \times \sqrt{1 + \frac{b^2}{a^2}}$.
• If b > a, the result is $b \times \sqrt{1 + \frac{a^2}{b^2}}$.

If the calculation of the absolute value results in an overflow, the method returns either Double.PositiveInfinity or Double.NegativeInfinity. If either the Real or Imaginary property is Double.NaN and the other property is neither Double.PositiveInfinity nor Double.NegativeInfinity, the method returns Double.NaN.

See also

• Magnitude