$e^{i\theta} = \cos\theta + i \sin\theta$ for solid angle steradian , working mechanism.

Question

$e^{i\theta} = \cos\theta + i \sin\theta$ for solid angle steradian , working mechanism. How will it work? For radian is 2D , i want for 3D.

Answer 1

Since 1steradian=1rad^2 $ e^{ix^2}=cos (x^2) + i sin (x^2)$. So put $\sqrt \pi$ steradian to get $e^{i\pi}=-1$.