Complex Coordinate Plane
How to graph complex numbers on a complex coordinate plane: examples and their solutions.
Complex Coordinate Plane
A complex coordinate plane has
an x-axis and an yi-axis.
The x-axis is the real number axis.
The yi-axis is the imaginary number axis.
So (a, bi) is the point
that shows x = a and yi = bi.
The [complex number] means
[real number] ± [imaginary number].
So the complex coordinate plane is used
to point complex numbers
on the complex coordinate plane.
Example 1: Graph 4 + 3i
4 + 3i is the point (4, 3i).
So draw (4, 3i)
on the complex coordinate plane.
Start from the origin.
The x value is 4.
So move 4 units to the right.
The yi value is 3i.
So move 3 units upward.
This point is (4, 3i).
It's like drawing (4, 3)
on a regular coordinate plane.
Coordinate plane
Example 2: Graph -5i
-5i, which is 0 - 5i, is the point (0, -5i).
So draw (0, -5i)
on the complex coordinate plane.
Start from the origin.
The x value is 0.
So don't move either to the left or to the right.
The yi value is -5i.
So move 5 units downward.
This point is (0, -5i).
Example 3: Graph (3 + 2i)i
Expand (3 + 2i)i.
3⋅i = 3i
+2i⋅i = +2⋅(-1)
Powers of i
+2⋅(-1) = -2
Write the real number part first.
Then (given) = -2 + 3i.
-2 + 3i is the point (-2, 3i).
So draw (-2, 3i)
on the complex coordinate plane.
Start from the origin.
The x value is -2.
So move 2 units to the left.
The yi value is 3i.
So move 3 units upward.
This point is (-2, 3i).
Let's see the meaning of multiplying i.
(3 + 2i)i = -2 + 3i
By multiplying i,
(3, 2i) moved to (-2, 3i).
(3, 2i) → (-2, 3i) shows
the rotation of 90º counterclockwise.
Rotation of 90º counterclockwise
So, by multiplying i,
the point on a complex coordinate plane
rotates 90º counterclockwise.
