# A compelling example of what complex numbers are for, before teaching them [duplicate]

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.

• @GeraldEdgar I don't think any of the answers to that question are suitable here. I can see they might have been suitable had people chosen to answer differently. – Anush May 24 '19 at 12:15
• – llllllllllllllllllllllllllllll May 24 '19 at 14:47
• @Anush Are there any really simple examples of tasks you can do, problems you can solve, using imaginary numbers but which you couldn't otherwise? The best motivation for complex numbers is the fundamental theorem of algebra (at least for me). – llllllllllllllllllllllllllllll May 24 '19 at 16:10
• As with many topics in math ... The uses for it are only seen much later. When a student starts to learn quantum mechanics, it is useful that she already knows complex analysis, and does not have to take a few months off to learn it then. – Gerald Edgar May 25 '19 at 10:58
• Anush There's a similar question asked yesterday math.stackexchange.com/q/3244132/81595 – llllllllllllllllllllllllllllll May 30 '19 at 20:56