Complex numbers can be visualized in the complex plane, also known as the Argand Diagram.

To plot a complex number, the real part determines the x-coordinate and the imaginary part determines the y-coordinate. Therefore the complex number a+bi has coordinates (a,b) on the plane.

It is conventional to use arrows from the origin to the point (a,b) to represent complex numbers.

Example

Find the complex number z labeled on the above complex plane.

We can see that z has x=Re(z)=4 and y=Im(z)=−1. So z=4−i