system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why are complex numbers so important?
gpt
Complex numbers are the combination of regular (real) numbers and imaginary numbers.

Quick primer: imaginary numbers themselves are just a place holder for something being multiplied by the square root of -1. So, instead of 5, you get 5i .  By themselves, they're alright, but what they can represent makes them important.

The cool thing about complex numbers is because they have both real (regular) parts and imaginary parts, they have lots of really convinient properties. For example, if you want to write an equation for a cirle, you can use lots of awkward hyberbolic trigonometry gobbeldy-gook, or you can very easily compress all of that info into a neat little expression of the form e^(i\*pi\*2).

Complex numbers also allow engineers and mathematicians to more easily represent things like electricity, radio waves, digital information, and stuff that repeats (think springs or swings).

TL;DR - Complex numbers make math more concise and easier to deal with.