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