log(x^3y^2)=3log(x)+2log(y)=3a+2b implies a=log(x) and b=log(y); log(x^2y^3)=2log(x)+3log(y)=2a+3b implies a=log(x) and b=log(y). Both equations have the same solution. Therefore x=p^a and y=p^b where p is the base of the logarithm. If p=e, the base of natural logs, then x=e^a and y=e^b.
(1+2i)/(1-(1-i)^2)=(1+2i)/(1-(1-2i-1))=(1+2i)/(1+2i)=1. |1|=1.