Why is $\displaystyle{W(-i\pi)}$ not equal to $\displaystyle{i\pi}$?

Question

The product log/Lambert's W $W(x)$ is defined as the inverse function of $\displaystyle{f(z)=ze^z}$. Since $-i\pi=e^{i\pi}\cdot i\pi$, why is $W(-i\pi)$ not equal to $i\pi$? My calculator+WolframAlpha instead give a number around $0.925+0.836i$.