I'm given poles at ${1+i}$ and ${1-i}$, and zero at $0$.
I have to find the difference equation and find out whether the system is stable.
Now I found in a similar question, which structure I tried to follow ( How to find system function, H(z) in the z-domain, given zero-pole plot of the system? ), that we can express $H(z)$ as $$H(z)=G_0z^{-1}\frac{(z-z_0)(z-z_1)\ldots}{(z-p_0)(z-p_1)\ldots} $$
It's clear to me that the numerator of H(z) is simply = z, but I can't wrap my head around the denominator.
I tried to go for: (z- (1-i))*(z- (1+i)) - my prof looked over my shoulder, nodded and told me to simply multiply it, adding "there will be no i in the polynomial". Now I really don't find any combination of tricks to achieve this, and I've been stuck for several hours right now.
I'd very much appreciate a hint!