Complex Coordinate Plane

Complex Coordinate Plane

How to graph complex numbers in a complex coordinate plane: examples and their solutions.

Example 1

Graph the given expression on the complex coordinate plane. 3 + 2i

The complex coordinate plane has
a horizontal real number axis (x-axis)
and a vertical imaginary number axis (yi-axis).

So 3 + 2i is on (3, 2i).

Draw (3, 2i)
like (3, 2) on the coordinate plane.

Example 2

Graph the given expression on the complex coordinate plane. 1 - 4i

1 - 4i is on (1, -4i).

Draw (1, -4i)
like (1, -4) on the coordinate plane.

Example 3

Graph the given expression on the complex coordinate plane. (3 + 2i)i

(3 + 2i)i = 3i + 2⋅(-1)
= -2 + 3i

It's on (-2, 3i).

See the effect of multiplying i.

By multiplying i,
(3 + 2i) is rotated 90º counterclockwise
and moved to (-2, 3i).

Rotation of 90º counterclockwise