Engineers use complex numbers to make communication systems work better, especially in a field called signal processing. Let’s break down how they do this:

1. Wave Representation: Signals can be shown as waves. Complex numbers make it easier to represent these waves. For example, a wave might be written as $A e^{i \omega t}$. In this, $A$ shows the height of the wave, $\omega$ represents how fast the wave is moving, and $t$ is the time.

2. Phasors: Engineers change signals that change over time into something called phasors. Phasors are special types of complex numbers that help show the height and position of waves more easily.

3. Analysis of Circuits: In electrical engineering, complex impedance combines resistance and reactance. This helps engineers analyze AC circuits better. It makes it simpler to figure out how voltage and current interact.

Using complex numbers not only makes calculations easier but also helps improve communication systems!