Find a sequence of complex numbers $\{z_k\}$ such that $\lim\limits_{k\to \infty} z_k = 0$ and $\lim\limits_{k\to \infty} e^{1/z_k} =2+i$.
i tried finding the logarithm of (2 + i) and I found it to be Log (2 + i) = ln √5 + i$\tan^{-1}(1/2)$.
I dont know what to do after this step. I saw the same question but they got $$e^{\ln \sqrt 3 +i \tan ^{-1} (1/2)}=2+i$$ and i got Log (2 + i) = ln $\sqrt{5}$ + i $\tan^{-1}(1/2)$.
Any help would be appreciated.