If $ arg(\bar{z_1}) = arg(z_2) $ , then

by

Q: If $ arg(\bar{z_1}) = arg(z_2) $ , then

(A) z2 = k z1-1 (k > 0)

(B) z2 = k z1 (k > 0)

(C) $ |z_2| = |\bar{z_1}|$

(D) None of these

Sol. $\large \bar{z_1} = \frac{z_1 \bar{z_1}}{z_1} = |z_1|^2 z_1^{-1} $

$\large arg(\bar{z_1}) = arg(|z_1|^2 z_1^{-1}) $

$\large arg(z_2) = arg(|z_1|^2 z_1^{-1}) $

Hence (A) is the correct answer .