complex function -singular points of function

Question

I'm trying to find which kind of singularity infinity is of the function

$$ f(z) = \frac{\cos(z + i) - 1}{(z + i)^4} $$

thanks

Answer 1

Verify that $f(\frac {n\pi} 2-i) \to 0$ whereas $|f(i(n-1))| \to \infty$. These facts imply that $f$ has an essential singularity at $\infty$.