Limit of a complex value function

Question

I am given that$f(x)=\frac{x^{2}i+e^{x}}{2^{x}+e^{x}i}$ I am trying to calculate the limit as $x$ tends to infinity. I have tried multiplying by the conjugate, L'Hopital's rule etc but I am not getting an answer.

Answer 1

We have $f(x)= \frac{e^x(1+i \frac{x^2}{e^x})}{e^x(i+( \frac{2}{e})^x)}=\frac{1+i \frac{x^2}{e^x}}{i+( \frac{2}{e})^x}.$

$\frac{x^2}{e^x} \to 0$ and $(\frac{2}{e})^x \to 0$ as $x \to \infty.$