12.33 If $|z|=1, \theta$ is the argument of $z$, then as $z$ varies, the image of $p=z^{2} +2 z \cos \theta$ in the complex plane is
(A) a circle.
(B) a hyperbola.
(C) a parabola.
(D) two intersecting lines.
(Chinese Jiangsu Province Suzhou City High School Mathematics Competition, 1990)