​ If (z - 1/z+1) is purely an imaginary number and z ≠ -1 then find the value of |z|. ​

Question

If \((\frac{z-1}{z+1})\) is purely an imaginary number and z ≠ -1 then find the value of |z|.

Answer 1

Given: \(\frac{z-1}{z+1}\) is purely imaginary number

Let z = x + iy

Now, rationalizing the above by multiply and divide by the conjugate of [(x + 1) + iy]

Putting i² = -1

Since, the number is purely imaginary it means real part is 0

∴ |z| = 1