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QuizMultiple Choice

Multiply and Divide Complex Numbers

Question 1 • NC-Math 4 CR

What is 56(cos(33°) + i sin(33°)) ÷ 7(cos(11°) + i sin(11°))?

Answer
A
8(cos(3°) + i sin(3°))
B
49(cos(3°) + i sin(3°))
C
8(cos(22°) + i sin(22°))
D
49(cos(22°) + i sin(22°))

Explanation

When dividing complex numbers in trigonometric form, divide their magnitudes and subtract their angles. Here, 56 ÷ 7 = 8 and 33° − 11° = 22°, so the quotient is 8(cos(22°) + i sin(22°)). This matches choice C.

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