(1-i)^2-2(1-i)+2

Question

its my math homework and i wanna know how?

Answer 1

(1-i)²=1-2i-1=-2i; -2(1-i)=-2+2i; so (1-i)²-2(1-i)+2=-2i-2+2i+2=0.

The answer is zero.

Another way is:

(1-i)²-2(1-i)+2=[(1-i)-1]²+1=i²+1=-1+1=0.