If $z$ is a complex number such that $z+\bar{z}=0$, then $z$ must be:

Solution

1. Let $z=x+iy$, where $x$ and $y$ are real numbers.
2. The conjugate is $\bar{z}=x-iy$.
3. The given condition is $(x+iy)+(x-iy)=0$.
4. This simplifies to $2x = 0$, which implies $x=0$.
5. Since the real part is zero, $z$ is purely imaginary.
6. Hence the answer is (B).