If α and β be the roots of the equation x^2-2x+2=0, then the least value of n for which (αβ)^n=1 is :

Correct option is C.
4x^2-2x+1+1=(x-1)^2+1=0
→(x-1)^2=i^2
→(x-1)=±i
x=(i+1) or (-i+1)
∴(αβ)^n=(i+1)(-i+1)^n →((i+1)^2)^n=(2i^2)^n=i^n=1
∴n (least natural number)=4