x^2 - 2x + 2
x = 1 + i
(1 + i)^2 - 2(1 + i) + 2
<em><u>Distributive property.</u></em>
(1 + i)(1 + i) - 2 - 2i + 2
<em><u>Continue distributive property on left side.</u></em>
1 + i + i + i^2 - 2 - 2i + 2
<em><u>Combine like terms.</u></em>
1 + 2i + i^2 - 2 - 2i + 2
1 + i^2
<em><u>i^2 can be interpreted as -1.</u></em>
1 - 1 = 0
The expression is equal to 0.