The complex number z which satisfies the condition|1+z/1-z| = 1 lies on

Question

The complex number z which satisfies the condition\(|\frac{1+z}{1-z}|\) = 1 lies on 

A. circle x² + y² = 1 

B. the x-axis 

C. the y-axis 

D. the line x + y = 1

Answer 1

Let, z = x + iy

x⁴+y⁴+1+2x² y²+2x²-2y²= x⁴+y⁴+1+2x² y²+2x²+ 6y²-4y³-2xy(x+y)-4y

8y² – 4y³ – 2xy(x + y) – 4y = 0

y(8y – 4y² – 2x(x + y) – 4) = 0 

y = 0 and 8y – 4y² – 2x(x + y) – 4 = 0

So, by y = 0 we can say that it lies on x axis