Question

How does the complex plane work$?$

Answer 1

Complex plane or argand plane :

The complex plane (also called the Argand plane or Gauss plane) is a way to represent complex numbers geometrically. It is basically a modified Cartesian plane, with the real part of a complex number represented by a displacement along the $x$-axis, and the imaginary part by a displacement along the $y$-axis.

Complex number represented: $z=x+iy$

Example:

$z=3+2i,$ where $x$ and $y$ are real numbers, and $i$ is the imaginary unit. In this customary notation the complex number $z$ corresponds to the point $\left(x,y\right)$ in the Cartesian plane.

Hence, the complex plane is basically a modified Cartesian plane where the $x$-axis and the $y$-axis have been dubbed the "real axis" and the "imaginary axis," respectively.