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: (3,5 / 3)
B: (3,  / 2)
C: (4, 5 / 6)




2. Give two equations for the first graph, and one equation for second graph.
a)
b)
Equation 1:
Equation :
Equation 2:
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MI 4 Polar Complex Exam
Name:
3. Solve the equation for z: (3  i ) z  3  4i  6  5i . Answer should be in a + bi form.
4. Let z1  4cis 120 and z2  2cis  50 . Find the following. State your answers in cis form.
a)
z12
z2
b)
z1·z2
1 i
c)
z13
z25
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MI 4 Polar Complex Exam
Name:
5. Find all solutions to the equation z 5  8 3  8i , then graph all roots on the grid below.
6. Convert each rectangular representation into its corresponding cis representation:
a.
12  5i
b.
2  3i
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MI 4 Polar Complex Exam
7.
Name:
Sketch the graph of r  2sin  3  , 0    
Label all points (using polar coordinates and being careful about domain: 0     )
where the graph is furthest from the pole (origin).
Find all values of  with 0     for which the graph passes through the pole .
Put arrows on each leaf (petal) indicating which doirection the petal is traced out as 
goes from 0 to  .
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