(1-i)^2(x+iy)
Well I don't think you can find the locus because I think there must be an equal sign for this.
Anyway, the working doesn't make sense to me ......
I can simplify it though.
\((1-i)^2(x+iy)\\ =(1-2i+i^2)(x+iy)\\ =(1-2i-1)(x+iy)\\ =-2i(x+iy)\\ =-2ix+-2i*iy\\ =-2ix+2y\\ =2y-2xi\\\)