If z is a complex number such that z-1 z+1 is purely imaginary, then what is |z| equal to?

Step-by-step solution

Let z=x+i y z-1 z+1 = (x-1)+i y (x+1)+i y = [(x-1)+i y] [(x+1)-i y] [(x+1)+i y] [(x+1)-i y] = (x^2-1 )+y^2+i[y(x+1)-y(x-1)] (x+1)^2+y^2 = (x^2+y^2-1 ) (x+1)^2+y^2 +i (2 y) (x+1)^2+y^2 It is purely imaginary, Re ( z-1 z+1 )=0 x^2+y^2-1 (x+1)^2+y^2 =0 x^2+y^2-1=0x^2+y^2=1|z|^2=1|z|=1