Download Ch 11 Study Guide (1)

DISCRETE STUDY GUIDE CHAPTER 11 NO CALCULATOR
Skills to know:












Be able to graph a point given its polar coordinates (11.1)
Rename a point using other polar coordinates (11.1)
Translate coordinates from rectangular to polar (11.1)
Translate coordinates from polar to rectangular (11.1)
Sketch a graph of polar functions (11.1)
Translate complex number to polar form (11.2)
Translate a complex number in polar form to rectangular form (11.2)
Perform the multiplication and Division of two complex numbers in polar form (11.2)
Apply DeMoivre’s Theorem to raise complex number to a power (11.3)
Graph a Complex number on the Complex Plane (11.3)
Find Roots of Complex Numbers (11.4)
REMEMBER YOUR TRIANGLES
1. Plot the points: A  3, 30  , B  4, 45
6

7 
 

,C  5,30  , D  1,  , E  4,

4 
 2

4
2
5
5
2
4
6
2. Give the coordinates of A so that:
6
a. r  0 and 0    2 _______________________
A
4
b. r  0 and 0    360 ______________________
c. r  0 and 360    720 __________________
d. r  0 and 2    0 ______________________
2
5
5
2
4
3. Translate(Convert) from rectangular to polar:
a. (2, 2√3)
b. (-6, -6)
4. Translate(Convert) from polar to rectangular:
a. (3,30 )
 3 
b. 12,

4 

6
5. Sketch the polar graphs:
Label key points, x and y intercepts
4
2
a. r  4  4sin 
5
5
2
4
6
6
b. r  3sin 6
4
2
5
5
2
4
6
c. r  3  4cos
6
4
2
5
5
2
4
6
d. r  4sin 
6
4
2
5
5
2
4
6
6. Write in polar form:
a. 𝑧 = −5 − 5𝑖√3
b. z  2i
7. Write in rectangular form:
a. z  5cis120
b. z  2cis90
8. Simplify to polar form and rectangular form:
a. (2𝑐𝑖𝑠(−30°))(−3𝑐𝑖𝑠165°)
b.
 6cis135  3cis15

3 

9. The product of  3cis
 and some other number is 2cis 270 . What is that other number written in
4 

rectangular form?
10. Let z  2  2i 3 . Compute the following: Remember the abs. value of z is equal to the radius or a
hypotenuse.
a. z =________________
b. z 5 =____________________ (Write answer in polar form only)
c.
z 4 =_________________
4
d. Graph 𝑧1 , 𝑧 2 , 𝑧 3 in an Argand diagram.
2
-5
5
-2
-4
-6
11. Describe how to find the nth roots of a complex number.
12. Find the 4th root of 16i