First find the 4 fourth roots of i, which are

, for n=0,1,2,3

. for n=0,1,2,3

Then taking 4th roots of both sides we have:

, for n=0,1,2,3

So

, for n=0,1,2,3 

Now substitute n=0,1,2, and 3 and simplify and you'll have the 
4 solutions.

Edwin