7
QuizMultiple Choice

Double-Angle and Half-Angle Identities — Unit test

Question 7 • LAUSD-Pre-Calculus B (Prescriptive)

What is the product of z1 and z2 if z1 = 2(cos70° + i sin70°) and z2 = 4(cos200° + i sin200°)?

Answer
A
6(cos270° + i sin270°)
B
8(cos14,000° + i sin14,000°)
C
8(cos70° + i sin70°)
D
8(cos270° + i sin270°)

Explanation

To multiply complex numbers in trigonometric form, multiply their magnitudes and add their angles. The magnitude is 2 × 4 = 8, and the angle is 70° + 200° = 270°. Therefore, the product is 8(cos270° + i sin270°), which is choice D.

AI-written and checked against the verified answer.

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