Complex.Acos(Complex) Method
Definition
Important
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Returns the angle that is the arc cosine of the specified complex number.
public:
static System::Numerics::Complex Acos(System::Numerics::Complex value);
public static System.Numerics.Complex Acos (System.Numerics.Complex value);
static member Acos : System.Numerics.Complex -> System.Numerics.Complex
Public Shared Function Acos (value As Complex) As Complex
Parameters
- value
- Complex
A complex number that represents a cosine.
Returns
The angle, measured in radians, which is the arc cosine of value
.
Examples
The following example illustrates the Acos method. It shows that passing the value returned by the Acos method to the Cos method returns the original Complex value.
using System;
using System.Numerics;
public class Example
{
public static void Main()
{
Complex[] values = { new Complex(.5, 2),
new Complex(.5, -2),
new Complex(-.5, 2),
new Complex(-.3, -.8) };
foreach (Complex value in values)
Console.WriteLine("Cos(ACos({0})) = {1}", value,
Complex.Cos(Complex.Acos(value)));
}
}
// The example displays the following output:
// Cos(ACos((0.5, 2))) = (0.5, 2)
// Cos(ACos((0.5, -2))) = (0.5, -2)
// Cos(ACos((-0.5, 2))) = (-0.5, 2)
// Cos(ACos((-0.3, -0.8))) = (-0.3, -0.8)
open System.Numerics
let values =
[ Complex(0.5, 2.); Complex(0.5, -2.); Complex(-0.5, 2.); Complex(-0.3, -0.8) ]
for value in values do
printfn $"Cos(ACos({value})) = {Complex.Acos value |> Complex.Cos}"
// The example displays the following output:
// Cos(ACos((0.5, 2))) = (0.5, 2)
// Cos(ACos((0.5, -2))) = (0.5, -2)
// Cos(ACos((-0.5, 2))) = (-0.5, 2)
// Cos(ACos((-0.3, -0.8))) = (-0.3, -0.8)
Imports System.Numerics
Module Example
Public Sub Main()
Dim values() As Complex = { New Complex(.5, 2),
New Complex(.5, -2),
New Complex(-.5, 2),
New Complex(-.3, -.8) }
For Each value As Complex In values
Console.WriteLine("Cos(ACos({0})) = {1}", value,
Complex.Cos(Complex.Acos(value)))
Next
End Sub
End Module
' The example displays the following output:
' Cos(ACos((0.5, 2))) = (0.5, 2)
' Cos(ACos((0.5, -2))) = (0.5, -2)
' Cos(ACos((-0.5, 2))) = (-0.5, 2)
' Cos(ACos((-0.3, -0.8))) = (-0.3, -0.8)
Remarks
The Acos method for complex numbers corresponds to the Math.Acos method for real numbers.
The Acos method uses the following formula:
(-ImaginaryOne) * Log(value + ImaginaryOne * Sqrt(One - value * value))