Question

Consider two complex numbers \( z_1 = 1 - i \) and \( z_2 = i \). The argument of \( z_1z_2 \) is:

• A. 0
• B. \(\frac{\pi}{4}\)
• C. \(\frac{\pi}{2}\)
• D. \(\pi\)

Hint:

When multiplying complex numbers, convert them to polar form for easier multiplication and determination of arguments.

Answer 1

The Correct Option is B

Multiply the complex numbers. \[ z_1z_2 = (1 - i) \cdot i = i - i^2 = i + 1 \] Step 2: Determine the argument.
The complex number \( i + 1 \) is in the first quadrant of the complex plane. The angle corresponding to a vector with equal real and imaginary parts is \(\frac{\pi}{4}\).