How many roots does the equation $z^{2018}=2018^{2018}+i$ have? 
Consider the equation
  $$ z^{2018}=2018^{2018}+i$$ where $i=\sqrt{-1}$.
  How many complex solutions as well as real solutions does this equation have?

My attempt:
I took the polar form as the equation has very difficult to handle when using $z=x+iy$.
So I set $z=re^{iθ}$, which yields
$$ (re^{iθ})^{2018}=2018^{2018}+e^{i\frac{\pi}{2}}$$
After this I was not able to handle it. 

There are several red herrings in the question and, as the problem is stated, you don't need to describe the solutions.
Your problem can be generalized to $z^n=a+i$, where $n$ is a positive integer and $a$ is real. Clearly, $z$ cannot be real, nor can $a+i$ be zero.
Thus the solutions are all complex (not real) and they are the $n$-th roots of $a+i$. There are $n$ of them.
