Q. If $z$ is a comple number such that $z = - z$, then
A) $z$ is purely real
B) $z$ is purely imaginary
C) $z$ is any complex number
D) Real part of $z$ is the same as its imaginary part
Explanation
(b)
Given, $z = - \overline{z}$
$\Rightarrow \ \ \ \ \ x + iy = - \overline{(x + iy)}$ [Put $z = x + iy$]
$\Rightarrow \ \ \ \ x + iy = - (x - iy)$
$\Rightarrow \ \ \ \ x = 0$
Hence, $z$ is a purely imaginary.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.