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.



Note

Also read this related article

Can check this video
https://www.youtube.com/watch?v=v52lvCN_pto