Can someone help me derive this equation using Euler's formula?

Question

$e^{a + bi} = e^a(\cos b + i \sin b)$ -- Euler's formula

Euler's formula gives rise to $e^{πi} + 1 = 0$ -- Equation

Five important numbers of $0, 1,\pi , e$, and $i$ are in this equation.

How can this equation be derived from using Euler's formula?

Answer 1

Hint:

Substitute $a+ib=0+\pi i$: $$ e^{0+\pi i }=e^0(\cos \pi+i\sin\pi) $$