# Chapter 4 Quadratic Functions and Factoring - 4.6 Perform Operations with Complex Numbers - Guided Practice for Examples 3, 4, and 5 - Page 278: 10

The impendence of the circuit is $5-4i$ ohms.

#### Work Step by Step

The resistor has a resistance of $5$ ohms, so its impedance is $5$ ohms. The inductor has a reactance of $3$ ohms, so its impedance is $3i$ ohms. The capacitor has a reactance of $7$ ohms, so its impedance is $-7i$ ohms. Hence, the impedance of the circuit is \begin{aligned} 5+3 i+(-7 i) &=5+3 i-7 i \\ &=5-4 i \end{aligned} So, the impedance of the circuit is $5-4 i$ ohms

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