Polar Form Of Complex Numbers Worksheet With Answer Key - Openstax College Page 16
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25OpenStax-CNX module: m49408
16
Exercise 44
(Solution on p. 19.)
1
z
= 3cis (120 ) ; z
=
cis (60 )
1
2
4
Exercise 45
π
π
z
= 3cis
; z
= 5cis
1
2
4
6
Exercise 46
(Solution on p. 19.)
5π
π
z
=
5cis
; z
=
15cis
1
2
8
12
Exercise 47
π
π
z
= 4cis
; z
= 2cis
1
2
2
4
z
For the following exercises, nd
1
in polar form.
z
2
Exercise 48
(Solution on p. 19.)
z
= 21cis (135 ) ; z
= 3cis (65 )
1
2
Exercise 49
z
=
2cis (90 ) ; z
= 2cis (60 )
1
2
Exercise 50
(Solution on p. 19.)
z
= 15cis (120 ) ; z
= 3cis (40 )
1
2
Exercise 51
π
π
z
= 6cis
; z
= 2cis
1
2
3
4
Exercise 52
(Solution on p. 19.)
2π
z
= 5 2cis (π) ; z
=
2cis
1
2
3
Exercise 53
3π
π
z
= 2cis
; z
= 3cis
1
2
5
4
For the following exercises, nd the powers of each complex number in polar form.
Exercise 54
(Solution on p. 19.)
3
z
z = 5cis (45 ) .
Find
when
Exercise 55
4
z
z = 2cis (70 ) .
Find
when
Exercise 56
(Solution on p. 19.)
2
z
z = 3cis (120 ) .
Find
when
Exercise 57
π
2
z
z = 4cis
.
Find
when
4
Exercise 58
(Solution on p. 19.)
3π
4
z
z = cis
.
Find
when
16
Exercise 59
3
5π
z
z = 3cis
.
Find
when
3
For the following exercises, evaluate each root.
Exercise 60
(Solution on p. 19.)
z
z = 27cis (240 ) .
Evaluate the cube root of
when
Exercise 61
z
z = 16cis (100 ) .
Evaluate the square root of
when
Exercise 62
(Solution on p. 19.)
2π
z
z = 32cis
.
Evaluate the cube root of
when
3
Exercise 63
z
z = 32
(π) .
Evaluate the square root of
when
cis
Exercise 64
(Solution on p. 19.)
7π
z
z = 8cis
.
Evaluate the cube root of
when
4
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