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