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

Step-by-step solution

x 2 - 2 x + 2 = 0 ⇒ ( x - 1 ) 2 + 1 = 0 ⇒ x = 1 ± i   ,   i = - 1 Now let the roots α = i + i   &   β = 1 - i α β n = 1 + i 1 - i n = i 1 - i 1 - i n ⇒ α β n = ( i ) n Using given information, ⇒ ( i ) n = 1 ⇒ The minimum value of n ∈ N = 4 because i 4 = 1 .