Download To multiply two complex numbers in polar form

Trigonometry Section 11.2
Write and graph complex numbers in polar form.
Multiply complex numbers.
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
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.
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
The length of the arrow
representing the complex
number is called the
absolute value of the
complex number.
|a+bi| = r =
Polar form:
4 cis 30o
5 cis π/2
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.
Theorem: To multiply two complex numbers in polar form:
1. Multiply their absolute values
2. Add their angles
(r cis α)(s cis β) = r∙s cis (α+β)
Multiply (3 cis 20o)(4 cis 50o)
Convert to polar form, multiply, change the product
back to rectangular form.
Z1 = 4 – 5i
Z2 = -2 + 6i
Assignment
• Page 406
• Problems 2 – 20 even