Question 744171
USING YOUR STRATEGY:
A simple equation with {{{1+i}}} and {{{1-i}}} for roots is
{{{(x-(1+i))(x-(1-i))=0}}} --> {{{(x-1-i)(x-1+i)=0}}} --> {{{(x-1)^2-i^2=0}}} --> {{{(x-1)^2+1=0}}} --> {{{x^2-2x+1+1=0}}} --> {{{highlight(x^2-2x+2=0)}}}
 
ANOTHER APPROACH:
x = 1 ± i --> x-1 = ± i --> {{{(x-1)^2=i^2}}} --> {{{x^2-2x+1=-1}}} --> {{{x^2-2x+1+1=0}}} --> {{{highlight(x^2-2x+2=0)}}}