complex analysis - Find $lim_{n to infty} n(frac{1+i}{2})^n$

Find $\lim_{n \to \infty} n(\frac{1+i}{2})^n$.

I don't know how to solve this limit. Should I use the fact that $\lim_{n \to \infty} n(\sqrt{2}/2)^n\cos(n \pi / 4)$ and $\lim_{n \to \infty} n(\sqrt{2}/2)^n\sin(n \pi / 4)$ for the real et imaginary part of $n(\frac{1+i}{2})^n$.

Can anyone give me a hint to solve the problem?