Tpc 2 Unit 1 Day 3 Multiplying Complex Numbers In Polar Form Worksheet Page 3
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1
2
3
4
5z = r(cos(θ) + isin(θ))
= r
(cos(nθ) + isin(nθ))
n
n
z
If
, then
where
n
i s
a
p ositive
i nteger.
When raising a complex number in polar form to a power “n”,
à We ________________ the value r to __________________
à We ________________ the
θ
value by _________________
DeMoivre’s theorem will enable you to find powers of a complex number expressed in polar form.
) + isin(72
o
o
5
Example 1: Evaluate
[2 cos(72
))]
.
Then express the answer in rectangular form.
) + isin(5 i 72
5
(cos(5 i 72
o
o
) + isin(72
=
o
o
5
2
))
[2 cos(72
))]
) + isin(360
0
o
=
32(cos(360
))
32(1+ i(0))
=
= 32
To apply DeMoivre’s Theorem, complex numbers must be in polar form.
4
Example 2: Find
(1+ i 3)
. Express the answer in rectangular form.
Step 1: Write
(1+ i 3)
in polar form.
θ
Step 2: Find r (Pythag) and
(trig ratio)
z = r(cos(θ) + isin(θ))
)
Step 3: Express in Polar Form
(
Step 4: Evaluate the power and put into rectangular (a+bi) form
Find each product or power and put final answer into a + bi form:
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