This document provides objectives and examples for converting complex numbers between trigonometric form and rectangular form, and for multiplying and dividing complex numbers in trigonometric form. It includes examples such as graphing and finding the magnitude of a complex number, writing a complex number at a given polar coordinate, and performing operations like multiplication and division on complex numbers expressed in trigonometric form. Students are assigned related practice problems to solidify their understanding.

1. 6.5 Complex Numbers in
Trigonometric Form
Objectives:
1) Convert complex numbers to trig form
and vice versa
2) Multiply/Divide complex numbers in trig
form.
Standard: Math Analysis 2.0

2. Ex. 1) Given: –2+4i
a) Graph
b) |–2+4i|
c) Find the inclination

3. Ex. 2) Given r=5 and θ=142°, find the
complex number a+bi at the same location.

4. θ
b
a
r

5. Trig Form Complex Form

6. Ex. 3) Write 6–6i in trig form.

7. Ex. 4) Write as a complex number.

8. Multiplying Complex Numbers in
Trig Form
Standard Form: (a+bi)(a+bi) = FOIL
Trig Form:

9. Ex. 5) Find z1z2.

10. Dividing Complex Numbers in
Trig Form
Standard Form: (a+bi)÷(a+bi)
= multiply by conjugate
Trig Form:

11. Ex. 6) Find

12. Assignment:
#6 p. 478
#12-39 (mult. of
3), 47-57 (odd)