Let z₁, Z₂ and z₃ be three complex numbers satisfying |z| = 1 and 4z₃ = 3(z₁ + z₂), then |z₁ - z₂| is equal to

Given that 4z₃ = 3(z₁ + z₂)

$\therefore \frac{{\mathrm{z}}_1+{\mathrm{z}}_2}{2}=\frac{2}{3}{\mathrm{z}}_3$

Therefore, mid-point of AB is the point which divides OM in the ratio 2 : 1.

or $\mathrm{OM}=\frac{2}{3}\mathrm{OC}=\frac{2}{3}\left|{\mathrm{z}}_3\right|=\frac{2}{3}$

$\therefore \left|{\mathrm{z}}_1-{\mathrm{z}}_2\right|=\mathrm{AB}=2\mathrm{AM}=2\sqrt{1-\frac{4}{9}}=\frac{2\sqrt{5}}{3}$