Question

If $z$ is a complex number satisfying $z+\overline{z}=0$, then

• A. $Im\left(z\right)=0$
• B. $Re\left(z\right)=0$
• C. $Im\left(z\right)=1$
• D. $Re\left(z\right)=1$

Answer 1

The correct option is B $Re\left(z\right)=0$

Let $z=x+iy$
$\Rightarrow \overline{z}=x-iy$

Given that $z+\overline{z}=0$
$\Rightarrow (x+iy)+(x-iy)=0\Rightarrow x=0\therefore Re\left(z\right)=0$