1. Trigonometric Form of Complex Numbers
Summary of U4 L2 I1

2. Graphical Representation of a Complex Number
Graph in coordinate plane
Called the complex plane
Horizontal axis is the real axis
Vertical axis is the imaginary axis
3 + 4i •
-2 + 3i •
• -5i

3. Absolute Value of a Complex Number
Defined as the length of the line segment
From the origin
To the point
Calculated by using Pythagorean Theorem
3 + 4i •

4. Find That Value, Absolutely
Try these
Graph the complex number
Find the absolute value

5. Trig Form of Complex Number
Consider the graphical representation
We note that a right triangle is formed
a + bi • r b θ a
How do we determine θ?

6. Trig Form of Complex Number
Now we use and substitute into z = a + bi
Result is
Abbreviation is often

7. Try It Out Given the complex number -5 + 6i Given z = 3 cis 315°
Write in trigonometric form
r = ?
θ = ?
Given z = 3 cis 315°
Write in standanrd form
a = ?
b = ?

8. Product of Complex Numbers in Trig Form
Given
It can be shown that the product is
Multiply the absolute values
Add the θ's

9. Quotient of Complex Numbers in Trig Form
Given
It can be shown that the quotient is

10. Try It Out Try the following operations using trig form
Convert answers to standard form