Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the given power. Write
answer in rectangular form.
(1
- i)10
a. | 32 | c. | 32 - 32i | b. | -32i | d. | -32 + 32i |
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2.
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Find the given power. Write
answer in rectangular form.
(-
 + i)6
a. | -64 | c. | -64 +
64i | b. | 64 - 64 i | d. | 64i |
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3.
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Find the given power. Write
answer in rectangular form.
(2
- 2i)5
a. | -64 +
64i | c. | -64 + 64 i | b. | -128 + 128i | d. | -  +  i |
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4.
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Find the given power. Write
answer in rectangular form.
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5.
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Find the given power. Write
answer in rectangular form.
a. | 64 + 12i | c. | 512 | b. | 64 | d. | -4 + 4i |
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6.
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Find all cube roots of the
complex number. Leave answers in trigonometric form.
64 cis 120°
a. | 4 , 4 , 4 | b. | 4(.7660 + .6428i), 4(-.9397 + .3420i), 4(.1736 -
.9848i) | c. | 4(.6428 + .7660i), 4(-.3420 + .9397i), 4(.9848 -
.1736i) | d. | 4 , 4 , 4 |
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7.
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Find all cube roots of the
complex number. Leave answers in trigonometric form.
64i
a. | 4 cis 0°, 4 cis 120°, 4
cis 240° | c. | 4 cis 60°, 4
cis 180°, 4 cis 300° | b. | 1, -1, -i | d. | 4 cis 30°, 4 cis 150°, 4 cis
270° |
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8.
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Find all cube roots of the
complex number. Leave answers in trigonometric form.
-8
a. | 2 cis 120°, 2 cis
180°, 2 cis 300° | c. | 2 cis 30°, 2 cis 150°, 2 cis
270° | b. | 2 cis 180°, 2 cis 0° | d. | 2 cis 60°, 2 cis 180°, 2 cis
300° |
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9.
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Find all cube roots of the
complex number. Leave answers in trigonometric form.
4 - 4i
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10.
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Find all specified
roots.
Cube roots of
1.
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11.
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Find all specified
roots.
Fifth roots of
1.
a. | -1, cis  , cis  , cis  , cis  | c. | 1, cis  , cis  , cis  ,-1 | b. | 1, cis  , cis  , cis  , cis  | d. | 1, cis  , cis  , cis  , cis  |
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12.
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Find all specified
roots.
Seventh roots of
1.
a. | 1, cis  , cis  , cis  , cis  , cis  , cis  | b. | -1, cis  , cis  ,
cis  , cis  , cis  , cis  | c. | 1, cis  , cis  , cis  , cis  , cis  , cis  | d. | 1, cis  , cis  , cis  , cis  , cis  , cis  ,
-1 |
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13.
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Find all specified
roots.
Cube roots of
i.
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14.
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Find all specified
roots.
Fifth roots of
i.
a. | cis  , cis  , cis  , cis  , cis  | c. | cis  , cis  , -1, cis  , cis  | b. | cis  , i, cis  , cis  , cis  | d. | cis  , cis  , cis  , cis  ,
1 |
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15.
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Find all specified
roots.
Eighth roots of
i.
a. | cis  , cis  , cis  , cis  , cis  , cis  , cis  , cis  | b. | 1, -1, i, -i | c. |  +  i,  -  i, -  +  i, -  -  i | d. | 1, -1 ,i, -i,  +  i,  -  i, -  +  i, -  -  i |
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16.
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Find all solutions of the
equation. Leave answers in trigonometric form.
 + 8 =
0
a. | {2 cis 180°, 2 cis 120°, 2
cis 300°} | c. | {2 cis 180°,
2 cis 240°, 2 cis 240°} | b. | {2 cis 180°, 2 cis 60°, 2 cis
300°} | d. | {2 cis 180°, 2 cis 120°, 2
cis 240°} |
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17.
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Find all solutions of the
equation. Leave answers in trigonometric form.
 + 8i =
0
a. | {2 cis 90°, 2 cis 210°, 2
cis 330°} | c. | {2 cis 270°,
2 cis 30°, 2 cis 150°} | b. | {2 cis 270°, 2 cis 210°, 2 cis
150°} | d. | {2 cis 90°, 2 cis 150°, 2
cis 30°} |
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18.
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Find all solutions of the
equation. Leave answers in trigonometric form.
 + 16 =
0
a. | { cis
45°,  cis 315°,  cis
135°,  cis
225°} | b. | {2 cis 45°, 2 cis 315°, 2 cis 135°, 2 cis
225°} | c. | { cis 26.565°,  cis
333.435°,  cis 153.435°, 
cis 206.565°} | d. | {16 cis 45°, 16 cis 315°, 16 cis 135°, 16 cis
225°} |
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19.
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Find all solutions of the
equation. Leave answers in trigonometric form.
 + 256i =
0
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20.
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A complex number z does not
belong to the Mandelbrot set if any of the complex numbers in the sequence z, 
 + z,  + z, ... has
modulus exceeding 2. Does  belong to the Mandelbrot
set?
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21.
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A complex number z does not
belong to the Mandelbrot set if any of the complex numbers in the sequence z, 
 + z,  + z, ... has
modulus exceeding 2. Does  belong to the Mandelbrot
set?
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22.
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A complex number z does not
belong to the Mandelbrot set if any of the complex numbers in the sequence z, 
 + z,  + z, ... has
modulus exceeding 2. Does  belong to the Mandelbrot
set?
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23.
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If n is an odd number, then
which of the following statements is true?
a. | The equation 
+ 1 = 0 has n + 1 roots. | b. | The equation  + 1 = 0 has an even number of real
roots. | c. | The equation  + 1 = 0 has exactly one real
root. | d. | The equation  + 1 = 0 has an odd number of nonreal
roots. |
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24.
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If n is an odd number, then
which of the following statements is true?
a. | The equation 
- 1 = 0 has exactly one real root. | b. | The equation  - 1 = 0 has n - 1
roots. | c. | The equation  - 1 = 0 has an even number of real
roots. | d. | The equation  - 1 = 0 has an odd number of nonreal
roots. |
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25.
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In which quadrants do the
nonreal cube roots of -1 lie?
a. | The first and fourth
quadrants | c. | The first and
third quadrants | b. | The second and third quadrants | d. | The second and fourth quadrants |
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26.
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In which quadrants do the
fourth roots of a complex number lie?
a. | The first and third quadrants if the
number is real and positive, and the second and fourth quadrants
otherwise | b. | The first and second quadrants if the number is real, and the third and fourth
quadrants if the number is not real | c. | All four quadrants | d. | The first and third quadrants if the number is real, and
the second and fourth quadrants if the number is not
real |
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27.
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What complex number is the
common cube root of -i and fourth root of 1?
a. |  | c. | -i | b. |  | d. | i |
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