Describe geometrically the three sets of points defined by the following equations in the complex $z$ plane:

(a) $z \bar{\alpha}+\bar{z} \alpha=0$, where $\alpha$ is non-zero;

(b) $2|z-a|=z+\bar{z}+2 a$, where $a$ is real and non-zero;

(c) $\log z=\mathrm{i} \log \bar{z}$.