The least positive integer n for which (1+i√3)/(1−i√3)^n=1, is

first rationalize the number
(1+i√3)/(1−i√3) × (1+i√3)/(1+i√3) = (1+i2√3+i²3)/(4) = (1−3+i2√3)/(4) = (−2+i2√3)/(4) = (−1+i√3)/2
(1+i√3)/(1−i√3) × (1−i√3)/(1−i√3) = (4)/(1+3) = 1/1
using (1) and (2)
(1+i√3)/(1−i√3)³ = (1+i√3)/(1−i√3) × (1+i√3)/(1−i√3) × (1+i√3)/(1−i√3) = (1+i√3)/(1−i√3) × ( −1+i√3)/2 × (−1+i√3)/2 = 1
Therefore correct Answer is 3
so correct option is 3