Complex Coordinate Plane

How to graph a complex number on the complex coordinate plane: definition, 2 examples, and their solutions.

Definition

Definition

The complex coordinate plane has
the x-axis and the yi-axis.

x-axis: Real number axis
yi-axis: Imaginary number axis

A complex number a + bi
is on the complex coordinate plane
at (a, bi).

Coordinate Plane

Example 1

Example

Solution

The given number is 4 + 3i.

The real number part is 4.

So start from the origin.
And move 4 units to the right.

The imaginary number part is +3i.

So move 3 units upward.

This is the point (4, 3i).

Example 2

Example

Solution

The given number is -5i.

The real number part is 0.

So start from the origin.
And don't move
either to the left or to the right.

The imaginary number part is -5i.

So move 5 units downward.

This is the point (0, -5i).