Check this out sci. Given the Euler formula
$\cos(\theta)+ i\sin(\theta) = e^{i\theta}$
Let $a = cos(\theta)$
Let $b = sin(\theta)$
So we have $a + ib$. This is amazing, it is basically the standard rectangular notation out of nowhere! Boom.
So back to the Euler formula, if we express $\theta$ in terms of a or b, we can't we re-write it as
$a + ib = e^{i\arccos(a)} = e^{i\arcsin(b)}$
I've never seen this before so I feel like I am onto something important but can't quite place it.
???

Pic unrelated.