Tpc 2 Unit 1 Day 3 Multiplying Complex Numbers In Polar Form Worksheet Page 2
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5Multiplying Complex Numbers in Polar Form
When multiplying two complex numbers in polar form,
à We ________________ the r values
à We ________________ the
θ
values
) + isin(θ
) + isin(θ
)) = r
+ θ
) + isin(θ
+ θ
)) i r
r
(cos(θ
(cos(θ
r
(cos(θ
))
1
1
1
2
2
2
1
2
1
2
1
2
Example 1
Multiply and put final answer into a + bi form:
5(cos(45°) + i sin(45°)) • 2(cos(90°) + i sin(90°))
= 5 • 2 (cos(45° + 90°) + i sin(45° + 90°))
= 10(cos(135°) + i sin(135°))
<––– Polar Form Answer
= 10(–0.707 + i 0.707)
= –7.07 + 7.07 i
<––– a + bi Form Answer
For each problem, multiply and put final answer into a + bi form:
1. 4(cos(60°) + i sin(60°)) • 3(cos(120°) + i sin(120°))
2. 5(cos(150°) + i sin(150°)) • 2(cos(60°) + i sin(60°))
3. [8(cos(45°) + i sin(45°))] 2
DeMoivre’s Theorem
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