# What a kid learning about the basics of complex numbers can look like

My younger son s studying complex numbers in Art of Problem Solving’s Precalculus book. The book has a nice problem asking about cube roots:

Find the values of $z$ satisfying $z^3 = -4 \sqrt{2}$ + $4 \sqrt{2}*i$.

Although his first approach the the problem is not correct, it is interesting to see that he is close to grasping the geometric ideas about complex numbers:

In the last video he’s found 3 numbers that he thinks will satisfy the original equation. Here we check them and find that they don’t:

Seeing why his original solutions didn’t work allowed him to find his mistake from the first video and here he finds the correct solutions:

I really liked how this seemingly straightforward problem helped my son learn about complex numbers. It is always fun to see a kid starting to understand a subject right from the beginning!