Question:
Given two complex numbers, \( z_1 = 4 + 3i \) and \( z_2 = 2 - 5i \), the real part of \( z_1z_2 \) is \(\underline{\hspace{2cm}}\).
Given two complex numbers, \( z_1 = 4 + 3i \) and \( z_2 = 2 - 5i \), the real part of \( z_1z_2 \) is \(\underline{\hspace{2cm}}\).
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When multiplying complex numbers, expand and use \( i^2 = -1 \) to simplify the expression.
Updated On: Jan 9, 2026
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Correct Answer: -7
Solution and Explanation
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.
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