Question

Let \(Z_1 = -2 + 2i\) and \(Z_2 = 3i\), then:

• A. \(\text{Arg}(Z_1 Z_2) = \frac{-3\pi}{4}\)
• B. \(\text{Arg}(Z_1 Z_2) = \frac{3\pi}{4}\)
• C. \(\text{Arg}(Z_1 Z_2) = \frac{-\pi}{4}\)
• D. \(\text{Arg}(Z_1 Z_2) = \frac{5\pi}{4}\)

Hint:

Always identify which quadrant your final complex number lies in.
Since both parts of \(-6 - 6i\) are negative, the number is in the 3rd quadrant.
This means its principal argument must be a negative angle between \(-\frac{\pi}{2}\) and \(-\pi\).
Only \(-\frac{3\pi}{4}\) satisfies this condition.

Answer 1

The Correct Option is A