PRECALCULUS HONORS
9.3 QUIZ
NAME_____________________________
DATE___________________ PD______
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Show all work for credit. All problems are two points each. All answers should be
completely simplified unless noted otherwise.
𝑧
1. Find zw and 𝑤 in polar form. (0 ≤ θ ≤ 360˚)
z = 𝟑 − 𝟑𝒊
w = −𝟐 + 𝟐𝒊√𝟑
zw = _______________
𝑧
𝑤
= ________________
7
2. Find the exact value of |(−√2 + 𝑖) |.
__________________
3. Prove that (r cis α)(s cis β) = rs cis (α + β). Show & explain all steps for full credit.
4. Suppose that a + bi is multiplied by −𝟓√𝟑 + 𝟓𝒊. By how many degrees must the arrow
from (0, 0) to (a, b) be rotated to coincide with the arrow from (0, 0) to the product?
Explain your answer.
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5. Write the expression in simplified rectangular form.
(−√𝟑 − 𝒊)
𝟕
___________________
6. Use the graph of the roots of a complex number, z, to write each of the roots in
rectangular form and then find z in rectangular form whose roots are given.
roots: ______________________________
z = ______________
7. Find all the cube roots of 𝟑√𝟑 + 𝟑𝒊. Write your answers in rectangular form. Round
answers to the nearest hundredth.
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8. Find the exact area of the polygon whose vertices are the sixth roots of -64i.
area: ___________________
9. If one cube root of z is 6 – 6i, find the other two roots in polar form (0 ≤ θ ≤ 2π) without
finding z. Explain.
Other roots: _________________________
Extra Credit: Write √2 𝑐𝑖𝑠
𝜋
12
in exact rectangular form. (1pt)
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