The equation I m i z - 2 z - i + 1 = 0 , z ∈ C , z ≠ i represents a part of a circle having radius equal to :

Step-by-step solution

Let z = x + i y , then I m   i x - y - 2 x + y - 1 i   x - y - 1 i x - y - 1 i + 1 = y - 1   y + 2 + x 2 x 2 + y - 1 2 + 1 = 0 ⇒ 2 x 2 + 2 y 2 - y - 1 = 0 ⇒ x 2 + y 2 - y 2 - 1 2 = 0 Center ( 0 ,   1 4 ) Radius = g 2 + f 2 - c Radius =   1 16 + 1 2 =   9 16 = 3 4