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 satisfying + .
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!