If α and β be the roots of the equation x2-2x+2=0, then  the least value of n for which αβn=1 is

The given quadratic equation is x2-2x+2=0 Then, the roots of the this equation are 2±-42=1±i Now, αβ=1-i1+i=(1-i)21-i2=i So, αβ=i Now, αβn=in=1⇒n must be a multiple of 4 .  Hence, the required least value of n=4 .