Deceptive Complex Numbers Problem

Here is a nice complex numbers problem that is trickier than it first appears...
A square in the complex plane has vertices at 1, i, -1 and -i. Prove that for any two complex numbers u and v within the square, their product uv also lies within the square.
Here is the link to the StackExchange post about a polygon in the complex plane:
math.stackexchange.com/questi...

[@houbengui09]

Pretty crazy

[@MathsWithMrLim]

Very crazy