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Advanced Math
Polar Graphing Homework Packet
NAME____________
9.1: Polar Coordinates
Graph each of the following points, then give two other coordinates that name the same point:
1. [2.5, 0o]
4. [-2,

]
4
2. [3, -135o]
5. [1,
3. [-1, -30o]
5
]
4
6. [2,
 2
]
3
Graph each of the following polar equations:
7. r = 3
8.  = 60o
9. r = 4
Find the distance between the two points with the given polar coordinates:
10. P1[6, 90o] and P2[2, 130o]
11. P1[[-4, 85o] and P2[1, 105o]
Advanced Math
Polar Graphing Homework Packet
NAME____________
9.2: Graphs of Polar Equations
Graph each of the following equations and identify which type of graph they create:
1. r = 1 + cos 
4. r = 2 + 2sin 
2. r = 3sin3 
3. 1 + 2cos 
5. r = .5 
6. Challenge Problem:
Graph the system of polar equation, then use the graph to solve the system.
r = 1 + 2sin 
r = 2 + sin 
Advanced Math
Polar Graphing Homework Packet
NAME____________
9.3: Polar and Rectangular Coordinates
Find the rectangular coordinates for each point with the given polar coordinates:
1. [6, 120o]
2. [-4, 45o]
3. [4,

]
6
4. [0,
13
]
3
Find the polar coordinates for each point with the given rectangular coordinates:
5. (2, 2)
6. (2, -3)
7. (-3,
3)
8. (-5, -8)
Advanced Math
Polar Graphing Homework Packet
NAME____________
9.5: Simplifying Complex Number
Simplify:
1. i38
2. i-17
3. i433
4. (3 + 2i) + (4 + 5i)
5. (-6 – 2i) – (-8 – 3i)
6. (8 – i) – (4 – i)
7. (1 + i)(3 – 2i)
8. (2 – 3i)(5 +i)
9. (4 + 5i)(4 – 5i)
10. (3 + 4i)2
12. (2 + i)  (2 – i)
11. (4 + 3i)2 (1 – 2i)
13.
8  7i
1  2i
Advanced Math
Polar Graphing Homework Packet
NAME____________
9.6: The Complex Plane and Polar Form of Complex Numbers
Graph each number in the complex plane and find its magnitude:
1. z = 3i
3. -4 – 4i
2. z = 5 + i
Express each complex number in polar form:
4. 3 + 4i
5. -4 + 3i
7. 1 – i
6. -1 + i
Graph each complex number. Then express it in rectangular form:
8. 2(cos
3
3
+ isin
)
4
4
9. 4(cos
5
5
+ isin
)
6
6
10. 3(cos
4
4
+ isin
)
3
3
Advanced Math
Polar Graphing Homework Packet
NAME____________
Convert the following into the other 3 forms:
11. [-3, -135o]
12. 2.5(cos 1 + isin1)
Notes: 1 is in radians
13. (-3, 0)
14. -1 - i 3