MI 4 Polar Complex Exam
Name:
You may use a TI-30 calculator on this exam.
1. Plot and LABEL WITH THE GIVEN LETTER the following points in polar coordinates
on the given grid:
A: (2,  / 3)
B: ( 3,  / 2)
C: (4, 5 / 6)




2. Give two equations for the first graph, and one equation for second graph.
a)
b)
y



x








Equation 1:
r  4cos
Equation :
r  5  7cos
Equation 2:


r  4sin    
2

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MI 4 Polar Complex Exam
1 
 1
3. Calculate 

i
2 
 2
1 
 1

i

2 
 2
2013
 cis  45
Name:
2013
. Put your answer in rectangular form.

4. Let z1  4cis20 and z2  2cis10 . Find the following. State your answers in cis form.
a) z12
b)
z1·z2
i
c)
z1
z23
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MI 4 Polar Complex Exam
Name:
5. Find all solutions to the equation z 6  32 3  32i , then graph all roots on the grid below.
 3 1 
r 5cis (5 )  16 
 i   16cis (330  360 k )
2
2 

So, r  5 16cis (65  72 k ) 
r  5 16cis (65 ), 5 16cis (137 ), 5 16cis(209 ),
5
16cis (281 ), 5 16cis(353 )
6. Convert each rectangular representation into its corresponding cis representation:
a.
4  3i
b.
6  2i
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MI 4 Polar Complex Exam
7.
Name:
Sketch the graph of r  1  2cos
Label all points (using polar coordinates) where the graph intercepts the horizontal and
vertical axes.
Find all values of  with 0    2 for which the graph passes through the pole (origin).
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