Download Review Packet Test Coord Systems

NAME:__________________________________________________
DATE:________________
REVIEW: COORDINATE SYSTEMS
2-D, 3-D, Complex, Polar
POLAR
Plot each point with the given polar coordinates.
1. (3, 45)
Rename #1 and #2 three different ways.
3. (3, 45)
2 

2.  3,

3 

2 

4.  3,

3 

________ or ________ or ________
________ or ________ or ________
Find the rectangular coordinates of #5 and #6. USE EXACT VALUE IF POSSIBLE!
5. (3, 45) = __________
2

6.  3,
3


 = __________

Find the polar coordinates for each point with the given rectangular coordinates.
USE EXACT VALUE IF POSSIBLE!
7. 3, 3
8. (2, -2)


Graph by hand (no y = button!), showing every 15 or
9. r  5sin(2 )

.
12

r

r
3D THREE DIMENSIONAL

z

10. Write the equation of a sphere with center at  3,5, 2 and radius of 7.
11. Plot the following points, find the midpoint and distance between them.
A(3,5,4)
B(4,6,3)
12. Find the intercepts of the following: 2 x  3 y  7 z  48
COMPLEX
13. Solve and graph the solutions in the complex plane.
Convert each complex number to polar form.
10. 1 – i
11. 2 3  2i
Convert each complex number in rectangular form.
12. 3(cos 45  i sin 45)
 2 
13. 3cis 

 3 
Find all possible roots of x 3  8 . Express solutions in rectangular form.
y
x
Exponential Form
re i  r (cos   i sin  )
For 1-9 use the point z1  2e
2
i
3
De Moivre’s Theorem
rcis n  r n cos n  i sin n 
and z 2  4cis 60
1. Convert z1 to complex polar (trigonometric form). Then graph it!
2. Convert z1 to complex rectangular. Then graph it on the complex plane!
3. Find the absolute value of z1 .
4. Find z1 z 2  . Express your answer in rectangular form.
5. Find
z1
. Express your answer in rectangular form.
z2
6. Find z1  z 2 . Express your answer in rectangular form.
7. Find z1  . Express your answer in rectangular form.
6
8. Find  z1  5 . Express your answers in trigonometric form.
1
9. Find the 5th root of z1 . Express your answer in trigonometric form.
SOLVE. Graph your solutions on the complex plane.
10. x   9
11. x 2  2 x  3  0
12. x 8  256
13. x 3  5i
MATCHING
14.
15.