# Complex Impedance

Complex impedances are commonly used quantities in the analysis of AC power systems. A complex impedance is represented by the following relation:

Where is the complex impedance ()

- is the resistance ()
- is the reactance ()
- is the complex component, i.e. )

For more details about why complex quantities are used in electrical engineering, see the article on complex electrical quantities.

## Complex Arithmetic

The manipulation of complex impedances follow the rules of complex arithmetic.

### Series Impedances

Two impedances in series can be combined by simply adding the individual real and complex terms (i.e. resistance and reactance components). For example, given:

Then,

### Parallel Impedances

Two impedances in parallel can be combined according to the following standard relation:

However, note that the multiplication and division of complex numbers is more involved than simply multiplying or dividing the real and complex terms:

**Multiplication:**involves multiplying cross-terms, i.e.

**Division:**involves multiplying by the complex conjugate of the denominator, i.e