`(z-alpha)/(z+alpha)` is purely imaginary and `|z|=82` then `|alpha|` is:

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alpha in RR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3

if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alpha)/(2)) is purely imaginary then alpha is given by -

If z is a purely imaginary number then arg (z) may be

The complex number z is purely imaginary , if

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+ 1/z is

If (z-1)/(z+1) is a purely imaginary number (z ne - 1) , then find the value of |z| .

If |z|=1 , then prove that (z-1)/(z+1) (z ne -1) is a purely imaginary number. What is the conclusion if z=1?

If (z+1)/(z+i) is a purely imaginary number (where (i=sqrt(-1) ), then z lies on a