An electrical network is an interconnection of analog electrical elements such as resistors, inductors, capacitors. The goal is to apply a predefined operation on voltages or currents.
Typical functions for electrical networks are amplification, analog linear algorithmic operations (addition, subtraction, multiplication, division, differentiation, integration), oscillators.
To design electrical circuits, electrical engineers need to be able to predict the voltages and currents in the circuit. For this they use Kirchhoffs Current Law and Ohms Law among others.
Complex number theory gave engineers the ability to treat all linear elements using a single mathematical representation.