When talking to kids before they are taught complex numbers, I would really like to give some examples of why it will be exciting to learn them. I am comfortable explaining the intellectual excitement and mystery but it would be great to combine that with real practical examples.

Are there any really simple examples of tasks you can do, problems you can solve, using imaginary numbers but which you couldn't otherwise?

By way of comparison, you can motivate negative numbers (to even younger children) simply by talking about going backwards, or paying back money etc.