Find the value of $a^4-a^3+a^2+2$ when $a^2+2=2a$ Find the value of $a^4-a^3+a^2+2$ when $a^2+2=2a$
My Attempt, 
$$a^4-a^3+a^2+2=a^4-a^3+2a$$
$$=a(a^3-a^2+2)$$
What's next?

$a^4-a^3+a^2+2=(a^2+a+1)(a^2-2a+2)=0$.
We can check also $a=1+i$ and $a=1-i$.
