I used complex numbers to solve popular interview question.

It can be used to convince students that they are useful.

https://pratik.deoghare.com/complex-mars-rover.html

The explanation is easy and fun.

I recommend Visual Complex Analysis by Tristan Needham

Really? Of approximately one billion good, visual introductions to complex numbers, we're going to pick an article that appears to be substantially written by an LLM?

When I first learnt complex numbers in school, I couldn't understand their purpose or why they are called imaginary etc.

I checked where they are used and found examples of current, magnetism etc. But I couldn't understand, electricity is a measurable physical quantity, how can you use imaginary numbers there??

Then I searched internet and found a Stack Exchange answer telling the story and how, instead of, complex (sounds like difficult) or imaginary (sounds like not useful practically), if we had better terms for them, then it would have been easier for beginners to understand them more intuitively.

It's completely true in my case.

After learning usage of vectors, thanks to Godot, for rotation and movement, and then about matrix etc. I now feel like "complex" numbers etc. are the representation of data through multiple numbers where a single value (scalars) is not enough. I may not be right in strict mathematics terms, but at least that's how I was able to understand them.