AnswersMath 4Complex Numbers

Complex Numbers — Test Answers

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1
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Which letter represents the result of subtracting z sub 2 from z sub 1 ?

A
cap b
B
cap A
C
cap d
D
cap c
2
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Given z sub 1 is equal to 5 minus 2 i and z sub 2 is equal to 3 plus 2 i , which letter represents z sub 1 minus z sub 2 ?

A
cap A
B
cap c
C
cap d
D
cap b
3

What is the difference between z sub 1 and z sub 2 , and where is the difference located?

A
difference: 0 plus 4 i ; location: on the imaginary axis
B
difference: 0 plus 4 i ; location: on the real axis
C
difference: negative 10 plus 0 i ; location: on the imaginary axis
D
difference: negative 10 plus 0 i ; location: on the real axis
4

Suppose z sub 1 is equal to 7 minus 3 i and z sub 2 is equal to 3 minus 5 i Which letter represents the sum z sub 1 plus z sub 2 ?

A
cap d
B
cap b
C
cap c
D
cap A
5

Which values of p and q would make the value of the following expression equal to 58 i ? open paren 3 minus 7 i close paren times open paren p plus q i close paren times i

A
p is equal to 3 , q is equal to negative 7
B
p is equal to negative 3 , q is equal to negative 7
C
p is equal to negative 3 , q is equal to 7
D
p is equal to 3 , q is equal to 7
6

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22 i Which statement must be true about the complex numbers?

A
The complex numbers have equal imaginary coefficients.
B
The complex numbers have opposite imaginary coefficients.
C
The complex numbers have opposite real numbers.
D
The complex numbers have equal real numbers.
7

What is the value of the fraction with numerator 15 i and denominator 2 plus i ?

A
negative 3 plus 6 i
B
5 plus 5 i
C
3 plus 6 i
D
5 minus 5 i
8

Given w is equal to square root of 2 times open paren cosine of open paren pi over 4 close paren plus i sine open paren pi over 4 close paren close paren and z is equal to 2 times open paren cosine of open paren pi over 2 close paren plus i sine open paren pi over 2 close paren close paren , what is w minus z expressed in polar form?

A
square root of 2 times open paren cosine of open paren 7 pi over 4 close paren plus i sine open paren 7 pi over 4 close paren close paren
B
square root of 2 times open paren cosine of open paren 3 pi over 4 close paren plus i sine open paren 3 pi over 4 close paren close paren
C
square root of 2 times open paren cosine of open paren pi over 4 close paren plus i sine open paren pi over 4 close paren close paren
D
square root of 2 times open paren cosine of open paren 5 pi over 4 close paren plus i sine open paren 5 pi over 4 close paren close paren
9

What is the additive identity of the complex number 14 plus 5 i ?

A
1
B
0
C
negative 14 minus 5 i
D
14 minus 5 i
10

Consider w sub 1 is equal to 4 plus 2 i and w sub 2 is equal to negative 1 minus 3 i Which graph represents the sum w sub 1 plus w sub 2 ?

A
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) downward to the right and ends at a filled point at (3 comma negative 5).
B
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) downward to the right and ends at a filled point at (3 comma negative 1).
C
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) upward to the right and ends at a filled point at (5 comma 5).
D
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) upward to the right and ends at a filled point at (5 comma 1).
11

Which expression is equivalent to the fraction with numerator 10 i and denominator 2 minus i ?

A
negative 5 i minus 2
B
4 i minus 2
C
negative 4 i minus 2
D
5 i minus 2
12

Which pair of complex numbers has a real-number product?

A
open paren 1 plus 2 i close paren times 4 i
B
open paren 1 plus 2 i close paren times 8 i
C
open paren 1 plus 2 i close paren times open paren 1 minus 2 i close paren
D
open paren 1 plus 2 i close paren times open paren 2 minus 5 i close paren
13

Daine simplified the expression. 8 times open paren 1 plus 2 i close paren minus open paren 7 minus 3 i close paren is equal to 1 plus 5 i What mistake did Daine make?

A
He did not apply the distributive property correctly for 8 times open paren 1 plus 2 i close paren .
B
He added the real number and coefficient of i in 8 times open paren 1 plus 2 i close paren .
C
He multiplied the two complex numbers when he should have subtracted.
D
He did not distribute the subtraction sign correctly for 7 minus 3 i .
14

What is the value of the product open paren 4 minus 2 i close paren times open paren 6 plus 2 i close paren ?

A
28 minus 4 i
B
20 minus 4 i
C
20 plus 16 i
D
28 plus 16 i
15

Let z is equal to 8 times open paren cosine of open paren pi over 3 close paren plus i sine open paren pi over 3 close paren close paren and w is equal to 3 times open paren cosine of open paren pi over 6 close paren plus i sine open paren pi over 6 close paren close paren . Which statement describes the geometric construction of the product z w on the complex plane?

A
Stretch z by a factor of 3 and rotate π6 radians counterclockwise.
B
Stretch z by a factor of 24 and rotate π6 radians counterclockwise.
C
Stretch z by a factor of 24 and rotate pi over 2 radians counterclockwise.
D
Stretch z by a factor of 3 and rotate pi over 2 radians counterclockwise.
16

Let z is equal to 9 minus 2 i and z w is equal to 25 plus 70 i What is w ?

A
1 plus 8 i
B
negative 1 plus 8 i
C
1 minus 8 i
D
negative 1 minus 8 i
17

Given z sub 1 is equal to square root of 2 times open paren cosine of open paren 3 pi over 4 close paren plus i sine open paren 3 pi over 4 close paren close paren and z sub 2 is equal to open paren cosine of open paren pi over 2 close paren plus i sine open paren pi over 2 close paren close paren , what is the value of z sub 1 minus z sub 2 ?

A
cosine of 0 minus i sine 0
B
cosine of pi minus i sine pi
C
cosine of 0 plus i sine 0
D
cosine of pi plus i sine pi
18

Let z is equal to 38 times open paren cosine of open paren pi over 16 close paren plus i sine open paren pi over 16 close paren close paren and w is equal to 2 times open paren cosine of open paren pi over 16 close paren plus i sine open paren pi over 16 close paren close paren What is the product of z w ?

A
76 times open paren cosine of open paren pi over 16 close paren plus i sine open paren pi over 16 close paren close paren
B
76 times open paren cosine of open paren 3 pi over 8 close paren plus i sine open paren 3 pi over 8 close paren close paren
C
40 times open paren cosine of open paren pi over 16 close paren plus i sine open paren pi over 16 close paren close paren
D
40 times open paren cosine of open paren 3 pi over 16 close paren plus i sine open paren 3 pi over 16 close paren close paren
19

What is the value of the fraction with numerator 6 i and denominator 1 plus i ?

A
2 plus 6 i
B
3 plus 3 i
C
2 minus 6 i
D
3 minus 3 i
20

What is the sum of 15 minus 6 i and negative 2 plus 9 i ?

A
13 plus 3 i
B
24 plus 147 i
C
17 plus 3 i
D
24 minus 147 i

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