Kuta Software - Infinite Precalculus
Name___________________________________
Complex Numbers and Polar Form
Date________________ Period____
Find the absolute value.
1) i
(
3)  cos
2)  i 


isin


)
(
 cos
4)


isin


)
Plot each point in the complex plane. Use rectangular coordinates when the number is given in
rectangular form and polar coordinates when polar form is used.
5) i

(
6)  cos
Imaginary











isin












 Real




)


















Convert numbers in rectangular form to polar form and polar form to rectangular form.
7)  i
9) 
11)
8)
10) i
   
 
i


(
 cos


isin


i 
)
(
12)  cos


isin


)
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Worksheet by Kuta Software LLC
13)


isin


(
 cos
)
 (cos isin  )
14)
Simplify. Write your answer in rectangular form when rectangular form is given and in polar
form when polar form is given.
15) (i)(i)
17)
(
16)   cos




isin
 cos isin




) (


isin


18)


 cos
isin


i
i
(
)
)
  cos
(
19) (i)
)

((
20)  cos


isin


))

Find all nth roots. Write your answers in rectangular form when rectangular form is given and in
polar form when polar form is given.
21) i, n
(
22)  cos


isin
, n


)
Critical thinking questions:
23) Show that i

n is a 23rd root of ni.
24) Solve for x : (i) xi
Hint: x is a complex number.
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Name___________________________________
Complex Numbers and Polar Form
Date________________ Period____
Find the absolute value.
1) i
2)  i 


(
3)  cos


isin


)
(
 cos
4)



isin


)

Plot each point in the complex plane. Use rectangular coordinates when the number is given in
rectangular form and polar coordinates when polar form is used.
5) i

(
6)  cos
Imaginary













isin









 Real





)


















Convert numbers in rectangular form to polar form and polar form to rectangular form.
7)  i
(
 cos
9) 
8)


isin


(
(
 cos


isin


(
  cos


isin


)
10) i
   
 
i




isin
 cos


11)
)
i 
)
)
 cos
(


isin


(


isin


12)  cos
i 
)
)
i 
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Worksheet by Kuta Software LLC
13)


isin


(
 cos
)
 (cos isin  )
14)
 


 
i


Simplify. Write your answer in rectangular form when rectangular form is given and in polar
form when polar form is given.
15) (i)(i)
(
(
16)   cos
i
  cos
17)




isin
 cos isin




) (
)


isin




isin


18)


 cos
isin


i
i
(
)
)
  cos
(
 
  i
 



cos  isin 



(
19) (i)
)

20)  cos


isin


 cos


isin


((
(
i
))
)
)

Find all nth roots. Write your answers in rectangular form when rectangular form is given and in
polar form when polar form is given.
21) i, n
(
22)  cos
i
i
i


isin
, n


)


isin





 cos
isin





 cos
isin





 cos
isin



(
(
(
(
 cos
)
)
)
)
Critical thinking questions:
23) Show that i

n is a 23rd root of ni.
(i  n )  = (i) (  n )  = in
 
24) Solve for x : (i) xi   i
Hint: x is a complex number.  
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Worksheet by Kuta Software LLC