I looked again at your work and found that you had not made a mistake where I had originally thought.  Further, your approach to solving the problem is much better than mine.  However, one thing I could not figure out is why you had not got credit for the solution.  The only thing I can come up with is that you made the assumption that y > x.  While this is true for real numbers, maybe it's not for the imaginary.

n can equal 1.67... or [-1.6727,10.92036]

So y/x = 1.618...   or  [-0.618..,4.983..]