​ Let a complex number be w = 1 – √3i . Let another complex number z be such that |zw| = 1 and arg(z) – arg(w) = π/2 . ​

Question

Let a complex number be w = 1 – √3i . Let another complex number z be such that |zw| = 1 and arg(z) – arg(w) = \(\frac{\pi}2\) . Then the area of the triangle with vertices origin, z and w is equal to :

(1) 4

(2) \(\frac 12\)

(3) \(\frac 14\)

(4) 2

Answer 1

Correct option is (2) \(\frac 12\)