The equation $\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$ represents a circle with :
centre at (0, $-$1) and radius $\sqrt 2 $
centre at (0, 1) and radius $\sqrt 2 $
centre (0, 0) and radius $\sqrt 2 $
centre at (0, 1) and radius 2