Equation of Circular Arc in Complex Plane

Theorem
Let $a, b \in \C$ be complex constants representing the points $A$ and $B$ respectively in the complex plane.

Let $z \in \C$ be a complex variable representing the point $Z$ in the complex plane.

Let $\lambda \in \R$ be a real constant such that $-\pi < \lambda < \pi$.

Then the equation:
 * $\arg \dfrac {z - b} {z - a} = \lambda$

represents the arc of a circle with $AB$ as a chord subtending an angle $\theta$ at $Z$ on the circumference.