Answer
$0$.
Work Step by Step
The given function is
$\Rightarrow f(x)=x^2-2x+2$.
Replace $x$ with $1+i$.
$\Rightarrow f(1+i)=(1+i)^2-2(1+i)+2$.
Use the distributive property and special formula $(A+B)^2=A^2+2AB+B^2$.
$\Rightarrow f(1+i)=1^2+2(1)(i)+i^2-2(1)-2(i)+2$.
Simplify.
$\Rightarrow f(1+i)=1+2i+i^2-2-2i+2$.
Use $i^2=-1$.
$\Rightarrow f(1+i)=1+2i-1-2-2i+2$.
Add like terms.
$\Rightarrow f(1+i)=0$.
