1. Trigonometry Section 11.2 Write and graph complex numbers in polar form. Multiply complex numbers.
To represent the complex number a+ bi graphically, use an Argand Diagram. The horizontal axis is the real axis and the vertical axis is the imaginary axis.
Recall: A complex number can be written in the form a+bi where i = √-1.
Graph the complex numbers using an Argand Diagram
Z1 = -3+4i
Z2 = 2-5i
Z3 = -4

2. Two ways to express a complex number Rectangular form: z = a+bi
Note: The complex number a+bi can be given in either rectangular form or in polar form.
Two ways to express a complex number
Rectangular form: z = a+bi
Polar form: z = r cos Θ + (r sin Θ)i
Abreviated polar form: z = r cis Θ
Polar form:
4 cis 30o
5 cis π/2
The length of the arrow representing the complex number is called the absolute value of the complex number.
|a+bi| = r =

3. Find the absolute value of -3 + 4i.
Express the complex number 3 cis 40o in rectangular form.
Express the complex number – 2 + 5i in polar form.

4. Theorem: To multiply two complex numbers in polar form:
Multiply their absolute values
Add their angles
(r cis α)(s cis β) = r∙s cis (α+β)
Multiply (3 cis 20o)(4 cis 50o)

5. Convert to polar form, multiply, change the product back to rectangular form.
Z1 = 4 – 5i Z2 = i

6. Assignment
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Problems 2 – 20 even