# Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 87

$2+3i$ ohms

#### Work Step by Step

We are given the voltage: $V=18+i$ and current $I=3-4i$. We find the impedance, Z: $\displaystyle Z=\displaystyle \frac{V}{I}$ $\displaystyle =\frac{18+i}{3-4i}$ $\displaystyle =\frac{18+i}{3-4i}*\frac{3+4i}{3+4i}$ $\displaystyle =\frac{54+72i+3i+4i^{2}}{9+12i-12i-16i^{2}}$ $\displaystyle =\frac{54+75i+4*-1}{9+16}$ $\displaystyle =\frac{50+75i}{25}$ $\displaystyle =2+3i$ ohms

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