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QuizMultiple Choice

Multiply and Divide Complex Numbers

Question 1 • CUSD Advanced Math A (5.0)

What is the product of 16(cos(47°) + i sin(47°)) and 4(cos(12°) + i sin(12°))?

Answer
A
20(cos(35°) + i sin(35°))
B
20(cos(59°) + i sin(59°))
C
64(cos(35°) + i sin(35°))
D
64(cos(59°) + i sin(59°))

Explanation

To multiply complex numbers in trigonometric form, multiply their magnitudes and add their angles. The magnitude is 16 × 4 = 64, and the angle is 47° + 12° = 59°. The product is 64(cos(59°) + i sin(59°)), which is choice D.

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