Math Test With Answers Page 3
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2
3
4Answer the question.
11) What complex number is the common cube root of -i and fourth root of 1?
A) -i
-i
B) i
C)
D)
i
Answer: B
Objective: (8.4) *Know Concepts: Powers/Roots of Complex Numbers
Find all cube roots of the complex number. Leave your answer in trigonometric form.
12) -5
3 + 5i
3
3
3
3
3
3
A)
10 cis 50°,
10 cis 170°,
10 cis 290°
B)
5 cis 70°,
5 cis 190°,
5 cis 310°
3
3
3
C)
5 cis 70°,
5 cis 190°,
5 cis 310°
D)
10 cis 50°,
10 cis 170°,
10 cis 270°
Answer: A
Objective: (8.4) Find Cube Roots of Complex Number
Answer the question.
13) If n is an even number, then which of the following statements is true?
A) The equation x n + 1 = 0 has at least one real root.
B) The equation x n + 1 = 0 has n + 1 roots.
C) The equation x n + 1 = 0 has exactly one real root.
D) The equation x n + 1 = 0 has n nonreal roots.
Answer: D
Objective: (8.4) *Know Concepts: Powers/Roots of Complex Numbers
Find all specified roots. Give your answer in trigonometric form.
14) Sixth roots of i.
Give your answer in trigonometric form with angles in radians.
A) cis 0, cis 3π
, cis 17π
, cis 25π
, cis 11π
4
12
12
4
B) cis π
, cis 5π
, cis 3π
, cis 13π
, 17π
, cis 7π
12
12
4
12
12
4
C) cis π
, cis 3π
, cis 17π
, cis 25π
, cis 11π
, cis 2π
12
4
12
12
4
D) cis 0, cis π
, cis 2π
, cis π, cis 4π
, cis 5π
3
3
3
3
Answer: B
Objective: (8.4) Find Specified Roots of 1, i (Trigonometric Form)
Solve.
15) A complex number z does not belong to the Mandelbrot set if any of the complex numbers in the sequence z,
z 2 + z, (z 2 + z) 2 + z, (z 2 + z) 2 + z 2 + z, ... has modulus exceeding 2. Does z = 2 belong to the Mandelbrot set?
A) No
B) Yes
Answer: A
Objective: (8.4) Solve Apps: Fractals (Y/N)
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