8
AssignmentMultiple Choice

Multiply and Divide Complex Numbers

Question 8 • NC-Math 4 CR

What is 6[cos(70°) + i sin(70°)] ÷ 2[cos(5°) + i sin(5°)]?

Answer
A
3[cos(75°) + i sin(75°)]
B
4[cos(75°) + i sin(75°)]
C
3[cos(65°) + i sin(65°)]
D
4[cos(65°) + i sin(65°)]

Explanation

To divide complex numbers in trigonometric form, divide their magnitudes and subtract their angles. The magnitude is 6 ÷ 2 = 3, and the angle is 70° − 5° = 65°. Therefore, the quotient is 3[cos(65°) + i sin(65°)], which is choice C.

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