In this post I’ll be proving why:
Let’s say that:
And also that:
This would imply that:
Now if we multiply and together, we get:
Which is thanks to what we know about trigonometric identities.
As we can see above, we’ve formed another complex number:
And this is in the form of:
And because of the rules of complex numbers, we can say that:
Hence, we have our proof.