Show that z=`frac{5}{(1-i)(2-i)(3-i)}` is purely imaginary number

If frac{z-i}{z+i}(z ne -i) is a purely imaginary number, then z.barz is equal to

If z is a complex number such that frac{z-1}{z+1} is purely imaginary, then

A Value of theta for which frac{2+3isintheta}{1-2isintheta} is purely imaginary is

If ( frac{z-1}{z+1} ) is a purely imaginary number (z != -1), then find the value of abs(z)

If frac{2z_1}{3z_2} is a purely imaginary number, then abs(frac{z_1-z_2}{z_1+z_2}) =

(frac{1+i}{1-i})^2 =?

Show that frac{1-2i}{3-4i} + frac{1+2i}{3+4i} is a real

Select and write the correct answer from the given alternatives in each of the following: The smallest positive integral value of n for which ((1 - i) / (1 + i))^n is purely imaginary with positive imaginary part is

The imaginary part of frac{(1+i)^2)(2-i) is

If z = x + i y and P represents z in the Argands plane. Find the locus of P when: (z - i) / (z - 1) is purely imaginary.