The equation a r g z - 1 z + 1 = π 4 represents a circle with:

Step-by-step solution

We have, a r g z - 1 z + 1 = π 4 a r g z 0 - 1 z 0 + 1 = π 2 ⇒ z 0 - 1 z 0 + 1 = e i π 2 ⇒ z 0 - 1 z 0 + 1 = i ⇒ z 0 = 1 + i 1 - i ⇒ z 0 = ( 1 + i ) 2 2 ⇒ z 0 = i ⇒ Centre 0 , 1 Radius is the distance between z 0 and - 1 , 0 = - 1 - 0 2 + 0 - 1 2 = 2   units