Deck 14: Complex Numbers

Question 1

Perform the addition or subtraction and write the result in standard form.​ $( 1.5 + 6.7 i ) + ( - 7.3 + 6.5 i )$ ​

A)​ $- 5.8 + 14.2 i$
B)​ $- 5.8 - 14.2 i$
C) $- 5.8 - 13.2 i$
D) $- 5.8 + 13.2 i$
E) $- 5.8 + 15.2 \mathrm { i }$

Answer 1

$- 5.8 + 13.2 i$

Question 2

Write the complex number in standard form.​ $3 - \sqrt { - 30 }$ ​

A)3 + $\sqrt { 30 }$ i​
B)4 + $\sqrt { 30 }$ i
C)7 - $\sqrt { 30 }$ i
D)3 - $\sqrt { 30 }$ i
E)4 - $\sqrt { 30 }$ i

Answer 2

3 - $\sqrt { 30 }$ i

Question 3

Perform the operation and write the result in standard form.​ $( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )$ ​

A)31
B)27
C)28
D)29
E)30

Answer 3

27

Question 4

Perform the operation and write the result in standard form.​ $$( 4 + 5 i ) ^ { 2 }$$ ​

A) $- 9 + 40 i$
B) $- 9 - 40 i$
C) $9 - 40 i$
D) $- 40 + 9 i$
E) $9 + 40 i$

Question 5

Write the complex number in standard form. ​​ $\sqrt { - 0.0001 }$ ​

A)​-0.01i
B)​​-0.0001i
C)​3.01i
D)​0.01i
E)​0.0001i

Question 6

Perform the operation and write the result in standard form.​ $( 1 + i ) ( 9 - 8 i )$ ​

A) $18 + i$
B) $17 + i$
C) $19 + i$
D) $21 + i$
E) $20 + i$

Question 7

Perform the addition or subtraction and write the result in standard form.​ $19 i - ( 15 - 3 i )$ ​

A)​ $15 + 22 i$
B)​ $- 15 - 22 i$ ​
C)​ $15 - 22 i$
D)​ $- 15 + 22 i$
E)​ $- 15 + 25 i$

Question 8

Perform the addition or subtraction and write the result in standard form. ​​ $( 12 - i ) - ( 7 - i )$ ​

A)5
B)7
C)9
D)8
E)​6

Question 9

Write the complex number in standard form.​ $8 + \sqrt { - 25 }$ ​

A)​ $8 + 25 i$
B)​ $11 - 8 i$
C)​ $11 + 8 i$
D)​ $8 - 5 i$
E)​ $8 + 5 i$

Question 10

Find real numbers a and b such that the equation is true.​ $a + b i = 2 + 6 i$ ​

A)​ $a = 4 , b = 8$
B)​ $a = 6 , b = 10$
C)​ $a = 2 , b = 6$
D)​ $a = 3 , b = 2$
E)​ $a = 5 , b = 9$

Question 11

Perform the addition or subtraction and write the result in standard form.​ $( 7 + i ) + ( 5 - 5 i )$ ​

A)16​ - 8i
B)​15 - 7i
C)​12 - 4i
D)​14 - 6i
E)​13 - 5i

Question 12

Write the complex number in standard form. ​
-4i + i²
​

A)​-1 + 4i
B)​-1 + 7i
C)​1 + 4i
D)​1 - 4i
E)​-1 - 4i

Question 13

Find real numbers a and b such that the equation is true. ​​ $( a + 4 ) + 2 b i = 4 - 17 i$ ​

A)​a = 0,b = - $\frac { 21 } { 2 }$
B)​​a = 0,b = - $\frac { 17 } { 2 }$
C)​​a = 0,b = - $\frac { 19 } { 2 }$
D)​​a = 0,b = -9
E)​​a = 0,b = -10

Question 14

Write the complex number in standard form.​ $\sqrt { - 36 }$ ​

A) $\sqrt { 37 }$ i
B)- $\sqrt { 39 }$ i
C) $6$ i
D) $\sqrt { 39 }$ i
E)- $6$ i

Question 15

Write the complex number in standard form.​ $\sqrt { - 17.64 }$ ​

A)17.64i
B)4.2i
C)​7.2i
D)-4.2i
E)-17.64i

Question 16

Perform the operation and write the result in standard form.​ $19 i ( 1 - 6 i )$ ​

A) $115 + 19 i$
B)​ $118 + 19 i$
C)​ $$116 + 19 i$$
D) $114 + 19 i$
E) $117 + 19 i$

Question 17

Find real numbers a and b such that the equation is true.​ $( a - 4 ) + ( b + 5 ) i = 13 + 11 i$ ​

A)​ $a = 20 , b = 9$
B)​ $a = 18 , b = 7$
C)​ $a = 19 , b = 8$
D)​ $a = 17 , b = 6$
E)​ $a = 21 , b = 10$

Question 18

Write the complex number in standard form.​ $\sqrt { - 36 }$ ​

A)6i
B)-6i
C)36i
D)7i
E)-36i

Question 19

Find real numbers a and b such that the equation is true.​ $a + b i = - 8 + 18 i$ ​

A) $a = - 12 , b = 22$
B) $$a = - 10 , b = 20$$
C)​ $a = - 11 , b = 21$
D) $a = - 9 , b = 19$
E) $$a = - 8 , b = 18$$

Question 20

Perform the addition or subtraction and write the result in standard form.​ $33 + ( - 10 + 13 i ) + 20 i$ ​

A)​ $23 + 33 i$
B)​ $23 - 33 i$
C)​ $- 23 - 33 i$
D)​ $- 23 + 33 i$
E)​ $23 + 35 i$

Question 21

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $5 + 3 i$ ​

A)​ $5 + 3 i , 34$
B)​ $5 - 3 i , 9$
C)​ $5 + 3 i , 9$
D)​ $- 5 - 3 i , 34$
E)​ $5 - 3 i , 34$

Question 22

Perform the operation and write the result in standard form.​ $( 8 - 7 i ) ^ { 2 }$ ​

A)​ $15 - 112 i$
B)​ $- 15 - 112 i$
C)​ $15 + 112 i$
D)​ $17 - 112 i$
E)​ $- 15 + 112 i$

Question 23

Solve the equation and write complex solutions in standard form. ​​ $x ^ { 2 } - 18 x + 91 = 0$ ​

A)​ $x = 9 + \sqrt { 10 } i , 9 - \sqrt { 10 } i$
B)​ $x = 10 + \sqrt { 2 } i , 10 - \sqrt { 2 } i$
C)​ $x = 9 + \sqrt { 2 } i , 9 - \sqrt { 2 } i$
D)​ $x = 10 + \sqrt { 10 } i , 10 - \sqrt { 10 } i$
E)​ $x = 2 + \sqrt { 10 } i , 2 - \sqrt { 10 } i$

Question 24

Write the quotient in standard form.​ $\frac { 4 + i } { 4 - i }$ ​

A) $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i
B) $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i
C) $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i
D) $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i
E) $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i

Question 25

Write the complex number in standard form.​ $\sqrt { - 6 } \cdot \sqrt { - 7 }$ ​

A)​- $\sqrt { 6 }$
B) $\sqrt { 7 }$
C) $\sqrt { 6 }$
D)- $\sqrt { 42 }$
E) $\sqrt { 42 }$

Question 26

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $\sqrt { - 39 }$ ​

A)-38i,39
B) $\sqrt { 39 }$ i,39
C)1521i,39
D)- $\sqrt { 39 }$ i,39
E)​-i,39

Question 27

Write the quotient in standard form.​ $- \frac { 20 } { 5 i }$ ​

A)​​4i
B) $\frac { 4 } { i }$
C)​ $- \frac { i } { 4 }$
D)​​-4i
E)​ $- \frac { 4 } { i }$

Question 28

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $2 - 14 i$ ​

A)​ $2 + 14 i , 196$
B)​ $2 - 14 i , 196$
C)​ $2 - 14 i , 200$
D)​ $- 2 + 14 i , 196$
E)​ $2 + 14 i , 200$

Question 29

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $- 14 + \sqrt { 13 } i$ ​

A)​ $- 14 - \sqrt { 13 } i , 209$
B)​ $14 - \sqrt { 13 } i , 209$
C)​ $- 14 + \sqrt { 13 } i , 209$
D)​ $14 + \sqrt { 13 } i , 209$
E)​ $- 13 - \sqrt { 14 } i , 209$

Question 30

Perform the operation and write the result in standard form. ​​ $\frac { 3 } { 1 + i } - \frac { 4 } { 1 - i }$ ​

A) $- \frac { 1 } { 2 }$ + $\frac { 2 } { 7 }$ i
B) $- \frac { 1 } { 2 }$ - $\frac { 2 } { 7 }$ i
C) $- \frac { 1 } { 2 }$ + $\frac { 7 } { 2 }$ i
D) $\frac { 7 } { 2 }$ $- \frac { 1 } { 2 }$ i
E) $- \frac { 1 } { 2 }$ - $\frac { 7 } { 2 }$ i

Question 31

Write the quotient in standard form.​ $\frac { 11 } { 1 - i }$ ​

A)​ $\frac { 11 } { 2 + i }$
B)​ $\frac { 11 } { 2 } i$
C)​ $\frac { 11 } { 2 - i }$
D)​ $\frac { 11 } { 2 } + \frac { 11 } { 2 } i$
E)​ $\frac { 11 } { 2 } - \frac { 11 } { 2 } i$

Question 32

Write the complex number in standard form.​ $\sqrt { - 20 } \times \sqrt { - 18 }$ ​ ​

A) $6 \sqrt { 10 }$
B) $- \sqrt { 20 }$
C) - $6 \sqrt { 10 }$
D) $\sqrt { 18 }$
E) $\sqrt { 20 }$

Question 33

Write the quotient in standard form.​ $\frac { 2 } { i }$ ​

A)​ $- \frac { i } { 2 }$
B)​ $- \frac { 2 } { i }$
C)​-2i
D)​ $\frac { i } { 2 }$
E)​2i

Question 34

Write the quotient in standard form. ​​ $\frac { 7 - 9 i } { i }$ ​

A)​ $- 7 - 9 i$
B)​ $- 9 - 7 i$
C)​ $- 9 + 7 i$
D)​ $9 - 7 i$
E)​ $9 + 7 i$

Question 35

Write the complex number in standard form.​ $( \sqrt { - 48 } ) ^ { 2 }$ ​

A) $- \sqrt { 48 }$
B)- $$48$$
C)​ $\sqrt { 23 }$
D) $48$
E)​ $\sqrt { 48 }$

Question 36

Write the complex number in standard form. $( 2 - \sqrt { - 15 } ) ^ { 2 }$

A) $- 11 + \sqrt { 15 } i$
B) $- 11 + 4 \sqrt { 15 } i$
C) $- 11 - \sqrt { 15 } i$
D) $- 11 - 4 \sqrt { 15 } i$
E) $4 - 15 \sqrt { 5 } i$

Question 37

Write the complex number in standard form.​ $( 4 + \sqrt { - 6 } ) ( 6 - \sqrt { - 14 } )$ ​

A)(24 - $2 \sqrt { 21 }$ )- (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i
B)(24 + $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i
C)(24 - $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i
D)(24 + $2 \sqrt { 21 }$ )- (6 $\sqrt { 6 }$ - 4 $\sqrt { 14 }$ )i
E)(24 + $2 \sqrt { 21 }$ )+ (6 $\sqrt { 6 }$ + 4 $\sqrt { 14 }$ )i

Question 38

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.​ $- 1 - \sqrt { 7 } i$ ​

A)​ $- 1 + \sqrt { 7 } i , 100$
B)​ $- 1 + \sqrt { 7 } i , 8$
C)​ $- 1 + \sqrt { 7 } i , - 6$
D)​ $1 - \sqrt { 7 i } , 100$
E)​ $1 + \sqrt { 7 } i , 8$

Question 39

Solve the equation and write complex solutions in standard form.​ $x ^ { 2 } + 10 x + 29 = 0$ ​

A)​ $x = 10 - 2 i , 10 + 2 i$
B)​ $x = - 2 - 5 i , - 2 + 5 i$
C)​ $x = - 5 + 4 i , - 5 - 4 i$
D)​ $x = - 5 - 2 i , - 5 + 2 i$
E)​ $x = - 2 + 25 i , - 2 - 25 i$

Question 40

Write the quotient in standard form. ​​ $\frac { 6 + 12 i } { 4 i }$ ​

A)3 - $\frac { 3 } { 2 }$ i
B)3 - 3i
C)3 $+$ $\frac { 3 } { 2 }$ i
D)3i - $\frac { 3 } { 2 }$
E)3i + $\frac { 3 } { 2 }$

Question 41

Do the operation and express the answer in a + bi form.Use fractions in your answer.​

Question 42

Do the operation and express the answer in a + bi form. ​
(5 - 5i)+ (8 + 3i)
​

A)2 - 13i
B)- 13 + 2i
C)13 + 2i
D)- 13 - 2i
E)13 - 2i

Question 43

Do the operation and express the answer in a + bi form.​ $\frac { - 19 } { i ^ { 36 } }$ ​

A)19i
B)- 19i
C)- 190i
D)- 19
E)19

Question 44

Simplify the complex number and write it in standard form.​ $\frac { 14 } { i ^ { 3 } }$ ​

A)​14i³
B)​​-14i³
C)​14
D)​​​-14i
E)​14i

Question 45

Do the operation and express the answer in a + bi form.​ $( 5 - \sqrt { - 25 } ) - ( 2 i - 3 )$ ​

A)- 8 + 14i
B)8 + 7i
C)- 8 + 7i
D)- 8 - 7i
E)8 - 7i

Question 46

Simplify the complex number and write it in standard form. ​​ $( 2 i ) ^ { 4 }$ ​

A)​16
B)​-16
C)​16i
D)​​-16i
E)​2i

Question 47

Simplify the complex number and write it in standard form.​ $3 i ^ { 2 } - 7 i ^ { 3 }$ ​

A)​ $- 7 + 3 i$
B)​ $3 + 7 i$
C)​ $- 3 - 7 i$
D)​ $- 3 + 7 i$
E)​ $3 - 7 i$

Question 48

Do the operation and express the answer in a + bi form.Do not use parentheses in your answer.
​
(3 - 8i)+ (10 + 5i)

Question 49

Simplify the complex number and write it in standard form.​ $( \sqrt { - 57 } ) ^ { 3 }$ ​

A)185,193i
B)-57i
C)- $57 \sqrt { 57 }$ i
D) $57 \sqrt { 57 }$ i
E)-185,193i

Question 50

Do the operation and express the answer in a + bi form.​ $( 9 - \sqrt { - 100 } ) + ( 10 + \sqrt { - 36 } )$ ​

A)19 - 4i
B)- 38 - 8i
C)19 + 4i
D)- 38 + 8i
E)- 19 + 4i

Question 51

Simplify the complex number and write it in standard form.​ $\frac { 1 } { ( 2 i ) ^ { 3 } }$ ​

A)​ $\frac { 1 } { 2 } i$
B)​ $- \frac { 1 } { 8 } i$
C)​ $\frac { 1 } { 8 } i$
D)​ $- \frac { 1 } { 2 } i$
E)​8i

Question 52

Describe the error.​ $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { ( - 8 ) ( - 8 ) } = \sqrt { 64 } = 8$ ​

A)​ $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i = - 8 i$
B)​ $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = - 64$
C)​ $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i$
D)​ $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i ^ { 2 } = - 8$
E)​ $\sqrt { - 8 } \sqrt { - 8 } = \sqrt { 8 } i \sqrt { 8 } i = 8 i ^ { 2 } = 8$

Question 53

Simplify the complex number and write it in standard form.​ $- 5 i ^ { 3 } + i ^ { 2 }$ ​

A)​ $1 + 5 i$
B)​ $- 1 - 5 i$
C)​ $- 5 i$
D)​ $1 - 5 i$
E)​ $- 1 + 5 i$

Question 54

Simplify the expression. ​
I ^-14
​

A)i
B)-3i
C)-i
D)-1
E)1

Question 55

Simplify the complex number and write it in standard form.​ $( - i ) ^ { 5 }$ ​

A)-1
B)​-i
C)​1
D)​i
E)5

Question 56

Raise the complex number to the fourth power. ​
​4i
​

A)​256
B)-64
C)64
D)16
E)-256

Question 57

Do the operation and express the answer in a + bi form.​ $( 5 + \sqrt { - 16 } ) ( 4 - \sqrt { - 4 } )$ ​

A)28 - 5 i
B)- 28 + 6 i
C)- 5 + 6 i
D)5 - 6 i
E)28 + 6 i

Question 58

Simplify the complex number and write it in standard form.​ $- 42 i ^ { 5 }$ ​

A)​ $- 42 i ^ { 3 }$
B)​ $42 i ^ { 3 }$
C)​ $- 42 i$
D)​ $- 42$
E)​ $42 i$

Question 59

Do the operation and express the answer in a + bi form.​ $\frac { 17 } { i ^ { 31 } }$ ​

A)-17i
B)-85i
C)-17
D)17i
E)17