Let $a, b, c$ be three complex numbers. The equation
$$az + b\bar{z} + c = 0$$
represents a straight line on the complex plane if and only if\\
(A) $a = b$\\
(B) $\bar{a}c = b\bar{c}$\\
(C) $|a| = |b| \neq 0$\\
(D) $|a| = |b| \neq 0$ and $\bar{a}c = b\bar{c}$