If P is the point in the argand diagram corresponding to the complex number root 3 + i and if OPQ is an isosceles right angled triangle, right angled at 0, then Q represents the complex number

Given P is the point in the argand diagram corresponding to the complex number √3 + i 

P is √3 + i 2(cos π/6 + i sin π/6)

Q1 is 2 (cos (π/2 + π/6)+ i sin(π/2 + π/6))

= 2 (- sin π/6 + i cos π/6)

= 2( -½ + i √3/2) 

= -1+i√3

Q2 is 2 (cos (π/6 – π/2)+ i sin(π/6 – π/2))

= 1-i√3

Hence option (1) is the answer.