Impedance in a Series Circuit

Impedance in an electronic circuit is measured using complex numbers. Below is a drawing of a series circuit with the meaning of the electronic symbols.

series circuit with key

If we use the variable r for resistance, m for the ohm value of the inductor, and c for the ohm value of the capacitor, the equation for the impedance of the circuit is Z = r + m·i - c·i where i=square root of -1 .

Example

series circuit with a resistor measuring 10 ohms, a capacitor measuring 15 ohms, and an inductor measuring 9 ohms.

Z = r + m·i - c·i, so Z = 10 + 9·i - 15·i, which implies Z = 10 - 6i

Problem

A series circuit has a resistor measuring 200 ohms, a capacitor measuring 40 ohms and a inductor measuring 50 ohms. What is the impedance of the circuit?