Electronic – How to calculate magnitude and phase different of impedence

impedance

How can I use a calculator to find the phase difference and magnitude of a circuit if the circuit has an impedance of, for example, \$Z = 5 + 3j\mbox{ }\Omega\$.

I have the answers \$|Z| = 5.83\$ and \$\theta = 30.96^{\circ}\$.

Best Answer

Euler is your friend. Euler's Formula:

\$ e^{j \theta} = cos(\theta) + j \cdot sin(\theta) \$

Euler helps you to calculate in an easy way with the complex impedance, by using the \$e\$ power. At the end of the calculation you can separate the complex power of \$e\$ into its real and imaginary parts. These agree with your resistance and reactive impedance resp.

\$ |Z| = \sqrt{real^2 + imaginary^2} \$

and

\$ \theta = arctan\left( \dfrac{imaginary}{real} \right) \$