If z-1/z+1 is purely imaginary, then | z | is​

Answer:|z| = 1

Solution :

Let z = x + iy. Then,

z−1z+1=(x−1)+iy(x+1)+iy×(x+1)−iy(x+1)−iy=(x2+y2−1)+(x+y)i(x+1)2+y2

Now, z−1z+1 is purely imaginary ⇔x2+y2−1=0⇔x2+y2=1⇔|z|=1.