Question

Given two complex numbers, \( z_1 = 4 + 3i \) and \( z_2 = 2 - 5i \), the real part of \( z_1z_2 \) is \(\underline{\hspace{2cm}}\).

Hint:

When multiplying complex numbers, expand and use \( i^2 = -1 \) to simplify the expression.

Answer 1

Correct Answer: -7

We need to find the real part of \( z_1z_2 \). First, compute \( z_1z_2 \): \[ z_1z_2 = (4 + 3i)(2 - 5i). \] Using the distributive property: \[ z_1z_2 = 4 \times 2 + 4 \times (-5i) + 3i \times 2 + 3i \times (-5i) = 8 - 20i + 6i - 15i^2. \] Since \( i^2 = -1 \), we have: \[ z_1z_2 = 8 - 20i + 6i + 15 = 23 - 14i. \] Thus, the real part of \( z_1z_2 \) is 23.