$\Gamma = { B\over e^{j\theta} -A}$
Both $A$ and $B$ are complex numbers.
The tedious way of course is to expand $A$, $B$ and $e^{j\theta}$, formulate the function into the form of $\Gamma = x + jy$, then prove $x^2 + y^2 = r^2$.
But I wonder whether there's a more clever way...
High school was such a long time ago and I find myself unable to come up with clever tricks any more...