In simplistic terms because if you plug [tex] \pi[/tex] into Euler's Formula the answer is -1

Euler's formula states that

[tex] e^{ix}=cos(x) + isin(x)[/tex]

as [tex]sin(\pi)= 0[/tex] and [tex]cos(\pi) = -1 [/tex] then [tex]e^{i\pi} = -1 + 0[/tex]

It can be demonstrated by using infinite series representations of both sides and showing they are equal.

The actual "how it comes about" for Euler's formula is difficult - but you could think of the two sides of [tex] e^{ix}=cos(x) + isin(x)[/tex] in terms of unit circles. [tex] cos(x) + sin(x)[/tex] traces a unit circle of circumference [tex] 2\pi[/tex] radians on the real number plane and conversely [tex]e^{ix}[/tex] could be said to trace a unit circle on the complex number plane as x varies through real numbers