If arg z - 10 + 6 i z - 4 + 2 i = π 4 (where z is a complex number), then the perimeter of the locus of z is

Step-by-step solution

Let A = 4,2 , B = 10,6 and C is the center of locus of z (which is a circle) ⇒ C A = C B = r a d i u s and ∠ A C B = 2 π 4 = π 2 ⇒ Δ A C B is right-angled isosceles triangle ⇒ r 2 + r 2 = 10 - 4 2 + 6 - 2 2 = 36 + 16 = 52 ⇒ r 2 = 26 ⇒ r = 26 ⇒ perimeter = 3 4 2 π r = 3 π 2 26 units