Q. If $(3 - i)z = (3 - i)\overline{z}$, then the complex number $z$ is
A) $a(3 - i),\ a \in R$
B) $\frac{a}{(3 + i)},\ a \in R$
C) $a(3 + i),\ a \in R$
D) $a( - 3 + i),\ a \in R$
Explanation
(a)
Given, $\frac{z}{\overline{z}} = \frac{3 - i}{3 + i}$ [let $z = x + iy$]
$\Rightarrow \ \ \ \ \frac{x + iy}{x - iy} = \frac{3 - i}{3 + i}\ \ \ \ \Rightarrow \ \ \ x = 3a,\ \ \ \ y = - a$
$\Rightarrow \ \ \ z = a(3 - i)$, where $a \in R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.