A complex variable is any variable in a complex number format. As it’s a complex number, it contains two components called real part and the imaginary component. To identify the imaginary part from the real part when they are both written together, we use the letter j or i on the left side of the imaginary component.

So, the general form of a complex variable is,

We can represent a complex vector graphically. Usually, the real component is represented by the x-axis while the imaginary component is represented by the y-axis.

Magnitude and Angle of a Complex Variable

We can also represent complex numbers and variables using the methods called rectangular form, and polar form. Before learning about those methods, you need to understand how to get the magnitude and the direction of a complex number.

Magnitude of a Complex Variable

The magnitude of a complex variable/ number is the distance from the complex plane’s origin. The magnitude, |z|, of a complex number, z = x + jy, is defined as |z| = √ (x² + y²).

Angle of a Complex Variable

The angle of a complex variable is the angle formed by a complex variable with the positive Real axis. And the complex angle is also known as the argument (arg).

Rectangular Form and the Polar Form Representation of Complex Variables

Rectangular form

A rectangular form of a complex variable is a representation as a point on the complex, a two-dimensional space.

Polar form

Complex numbers can also be represented in different ways, such as the polar form of a complex number. In polar form, complex numbers are represented as the combination of the modulus and the angle, which is known as the polar form.