# Complex Coordinate Plane

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

## Example 1

The complex coordinate plane has

a horizontal real number axis (*x*-axis)

and a vertical imaginary number axis (*yi*-axis).

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

Draw (3, 2*i*)

like (3, 2) on the coordinate plane.

## Example 2

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

Draw (1, -4*i*)

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

## Example 3

(3 + 2*i*)*i* = 3*i* + 2⋅(-1)

= -2 + 3*i*

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

See the effect of multiplying *i*.

By multiplying *i*,

(3 + 2*i*) is rotated 90º counterclockwise

and moved to (-2, 3*i*).

Rotation of 90º counterclockwise