If P z is a variable point in the complex plane such that Ιm - 1 z = 1 4 , then the value of the perimeter of the locus of P z is (use π = 3 . 14 )

Step-by-step solution

Ιm - z ¯ z 2 = 1 4 Let, z = x + i y , then z ¯ = x - i y ⇒ - - y x 2 + y 2 = 1 4 ⇒ x 2 + y 2 - 4 y = 0 Hence, locus is a circle ⇒ radius of circle is 2 ⇒ perimeter of circle is 4 π