Complex Numbers Worksheet With Answers Page 7
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2
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9
10π
π
a) (cos
3
+ i
sin )
2
2
DeMoivre’s Theorem Powers of Complex Numbers in Polar form:
Find the power of the complex number
Let
z
= r
(cosθ
+
i sinθ )
be a complex
o
o
5
A) 2(cos30
[
+ i
sin30 ) ]
number of polar form.
and be a positive integer
n
Then to the
z
n
th power
is found by:
n
n
z
= [
r(cosθ
+ i
sinθ) ]
n
= r
(cos nθ
+ i
sin nθ)
Find the powers in simplest form:
o
o
6
A)
[
2(cos20
+ i
sin20 ) ]
a)
− 3 + 3 √ 3
2
2i
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