Question

If $Z$ is a complex number such that $Z=-\overline{Z}$ , 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

Answer 1

Answer: (B)

Let $z=x+iy$ Given, $z=-\bar{z}$
$\therefore x+iy=-\overline{(x+iy)}$
$\Rightarrow x+iy=-(x-iy)$
$\Rightarrow 2x=0$
$\Rightarrow x=0$
Hence, $z$ is a purely imaginary.