For all z ∈ C on the curve C 1 : | z | = 4 , let the locus of the point z + 1 z be the curve C 2 . Then

Step-by-step solution

Given: C 1 : z = 4 ,   C 2 : z + 1 z Here, z = 4 is a circle x 2 + y 2 = 16 . Now, let z = 4 e i θ , So, z + 1 z = 4 e i θ + e - i θ 4 ⇒ x + i y = 4 cos θ + i 4 sin θ + cos θ 4 - i sin θ 4   taking  z + 1 z = x + i y Now on comparing both side we get, x = 17 4 cos θ   &   y = 15 4 sin θ Now on solving cos 2 θ + sin 2 θ = 1 we get, x 2 17 4 2 + y 2 15 4 2 = 1 Which is a equation of ellipse, Therefore, curves C 1 and C 2 interse