If P is the point in the Agrand diagram corresponding to the complex number 3 +i and if O P Q is an isosceles right angled triangle, right angled at ' O ', then Q represents the complex number

Step-by-step solution

Let z= 3 +i aligned ( z ) &= ⁻¹ ( 1 3 ) &=30^ aligned For making a right angled triangle OPQ, point Q either in IInd quadrant or IVth quadrant. If the point Q is in Ind quadrant, then we take =120^ aligned 120^ &=- 30^ &= 3 -1 aligned Point Q is (-1, 3 ) and if the point Q is in IVth quadrant, then we take aligned &=-60^ (-60^ ) &=- 60^ &=- 1 3 aligned Point Q is (1,- 3 ) . Hence, option (a) is correct.