Complex Numbers Worksheet With Answers Page 8
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10DeMoivre’s Theorem Powers of Complex Numbers in Polar form:
Find the power of the complex number using
Let
z
= r
(cosθ
+
i sinθ )
be a complex
DeMoivre’s Thm. Write the answer in rectangular form
number of polar form a+bi.
a+bi
and be a positive integer
n
4
A) 1
( + i
)
Then to the
is found by:
z
n
th power
n
n
z
= [
r(cosθ
+ i
sinθ) ]
You must find all parts of DeMoirve’s Theorem!
n
= r
(cos nθ
+ i
sin nθ)
a=_______ b= ________
r=____________ (beginning of today’s notes)
θ =
______________(beginning of today’s notes)
Now use the formula!
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