# Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 85

25

#### Work Step by Step

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate to obtain: $z*\overline{z}$ $=(3-4i)(\overline{3-4i})$ $=(3-4i)(3+4i)$ $=9+12i-12i-16i^{2}$ $=9-16*-1$ $=9+16$ $=25$

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