Let `z_(1),z_(2),z_(3),z_(4)` are distinct complex numbers satisfying `|z|=1` and `4z_(3) = 3(z_(1) + z_(2))`, then `|z_(1) - z_(2)|` is equal to

Options

A. 1 or i
B. `i or -i`
C. 1 or i
D. `i or -1`

Answer

D

Explanation

Given that `4z_(3) = 3(z_(1) + z_(2))`
`therefore (z_(1)+ z_(2))/(2)= (2)/(3)z_(3)`
Therefore, mid -point of AB is the point which divides OM is the ratio 2:1

or `OM = (2)/(3) OC = (2)/(3)|z_(3)|= (2)/(3)`
`therefore |z_(1)-z_(2)| = AB = 2AM = 2sqrt(1-(4)/(9))=(2sqrt(5))/(3)`