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Complex Numbers

The Infragistics Math Library™ provides functionality for working with Complex Number.

Types of Complex Numbers Operations

The operations supported by complex numbers fall into the following basic categories:

Creating the Imaginary Unit

The imaginary unit i can be created as a new complex number with a real part equal to 0 and an imaginary part equal to 1. The imaginary unit is also provided in the Constant class.

In Visual Basic:

'Create the imaginary unit
'using a new complex number.
Dim i As New Complex(0, 1)
'Creating the imaginary unit
'using the I contant.
Dim i As Complex = Constant.I

In C#:

//Create the imaginary unit
//using a new complex number.
Complex i = new Complex(0, 1);
//Creating the imaginary unit
//using the I contant.
Complex i = Constant.I;

Creating Complex Numbers

Complex numbers have one constructor, specifying the real and imaginary components of the number.

A less formal and less efficient way of constructing a complex number is to use the plus operator along with the imaginary unit.

The following code snippet demonstrates how to create a new Complex object using the constructor and the plus operator:

In Visual Basic:

'Creating a complex number
'using the constructor.
Dim z As New Complex(1, 1)
'Creating a complex number
'using the plus operator.
Dim z As Complex = 1 + 1 * Constant.I

In C#:

//Creating a complex number
//using the constructor.
Complex z = new Complex(1, 1);
//Creating a complex number
//using the plus operator.
Complex z = 1 + 1 * Constant.I;

The two variables titled z will be equivalent. The second notation is less computationally efficient because it involves the construction of Constant.I, plus an addition and multiplication operation.

Creating Complex Numbers Using Properties

Complex numbers have four properties, specifying their real and imaginary components, as well as their magnitude and phase. The following code demonstrates how to create of a complex number and use its properties to retrieve its real and imaginary parts, the magnitude, and the phase:

In Visual Basic:

Dim z As New Complex(1, 1)
Dim real As Double = z.Re
Dim imaginary As Double = z.Im
Dim magnitude As Double = z.Mag
Dim phase As Double = z.Phase

In C#:

Complex z = new Complex(1, 1);
double real = z.Re;
double imaginary = z.Im;
double magnitude = z.Mag;
double phase = z.Phase;

These functions also have static versions in the Compute class, though with slightly different names to specify their functional forms:

In Visual Basic:

Dim z As New Complex(1, 1)
Dim real As Double = Compute.Real(z)
Dim imaginary As Double = Compute.Imaginary(z)
Dim magnitude As Double = Compute.Abs(z)
Dim phase As Double = Compute.Arg(z)

In C#:

Complex z = new Complex(1, 1);
double real = Compute.Real(z);
double imaginary = Compute.Imaginary(z);
double magnitude = Compute.Abs(z);
double phase = Compute.Arg(z);

Mathematical Operations

The following operations are predefined for complex numbers:

  • Arithmetical Operations

    • addition (+)

    • subtraction (-)

    • multiplication (* )

    • division (/)

    • division with remainder (%)

  • Comparison Operations

    • equal to (==)

    • not equal to (!=)

    • greater than (>)

    • less than (<)

    • greater than or equal to (>=)

    • less than or equal to (<=)

Using Standard Mathematical Functions With Complex Numbers

The Compute class contains static methods, which represent all of the standard mathematical functions extended to use complex numbers. Following is a code example of several mathematical functions:

In Visual Basic:

Dim z As New Complex(1, 1)
Dim sinz As Complex = Compute.Sin(z)
Dim cosz As Complex = Compute.Cos(z)
Dim expz As Complex = Compute.Exp(z)
Dim logz As Complex = Compute.Log(z)

In C#:

Complex z = new Complex(1, 1);
Complex sinz = Compute.Sin(z);
Complex cosz = Compute.Cos(z);
Complex expz = Compute.Exp(z);
Complex logz = Compute.Log(z);

Related Topics

Vectors

Matrices

Mathematical Functions