show that 1+i is a solution for the equation x^2-2x+2=0
\((1+i)^2 =1^2+2i+i^2=1+2i-1=2i\\ -2(1+i)=-2-2i\\ so\\ (1+i)^2-2(1+i)+2\\ =2i-2-2i+2=0\\ \therefore\\ 1+i \quad \mbox{is a solution to }\;\;x^2-2x+2=0\)
