Evaluate x^2-2x+2 where x=1+i

x^2 - 2x + 2

x = 1 + i

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

Distributive property.

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

Continue distributive property on left side.

1 + i + i + i^2 - 2 - 2i + 2

Combine like terms.

1 + 2i + i^2 - 2 - 2i + 2

1 + i^2

i^2 can be interpreted as - 1.

1 - 1 = 0

The expression is equal to 0.