The Complex Plane (Cartesian Plane)

Complex plane can be thought to be modified Cartesian plane, with the real part of a complex number represented by a distance along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation of complex numbers. The real part of complex numbers is represented in the x-axis and Imaginary part in the y-axis

The Cartesian Plane:

The normal Cartesian plane, with x-axis and y-axis, is also used to represent the Complex Plane. The x-axis is the Real axis and y-axis is the Imaginary axis in the Complex Plane. The Diagram below shows the complex plane of
z = a + ib and its conjugate is z = a – ib.

Examples shown in the Diagram below are

a. z = a + ib                b. -z = a – ib                         cz = a – ib.  (conjugate)

complex palne
Complex plane in a Cartesian plane

The plot of the complex numbers z = 4 + 3i and z = -5 – 4i on the complex plane is as shown below

complex plane
complex plane of z = -5 + 4i and z = 4 + 3i

Complex numbers can be represented graphically on the complex plane. The resulting graphical representation of complex and Real numbers is called Argand Diagram.


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