I assume the function is actually .
Since you've found a factor, long divide to get the cubic factor. See if you can factorise that cubic.
I have a start on this polynomial:
If I let f(z) = f(-1) I will find that the expression equals zero and so (z+1) is a factor.
But where do I go from here?
The answer in the back of the book is (z+1)(z+1+2i)(z+1-2i)(z-3)