Complex Numbers Worksheet With Answers Page 9
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1
2
3
4
5
6
7
8
9
10Find the powers in simplest form:
8
A)
( + i
1
)
a) 6 or 16
+ 0
1
i
DeMoivre’s Theorem Roots of Complex Numbers in Polar form:
o
0
A) Find all complex fourth roots of
1
6(cos60
+ i
sin60 )
.
Let
w = r
(cosθ
+
i sinθ ) where w =
/ 0
be a
Write all roots in polar form with in degrees:
θ
complex number of polar form a+bi.
Then w has possible roots found by the
n
equations:
θ+2πk
θ+2πk
Radians:
z
= √
n
r
[cos(
)
+ i
sin (
)]
k
n
n
θ+2πk
θ+2πk
Degrees:
n
z
= √
r
[cos(
)
+ i
sin (
)]
k
n
n
where
k = 0
, 1, 2, 3, ..., n
− 1
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