If `z_1`, `z_2` and `z_3`, `z_4` are two pairs of conjugate complex numbers, then find arg(`frac{z_1}{z_4}`) + arg(`frac{z_2}{z_3}`)

The conjugate of the complex number z is frac{1}{i-1} then z=

If z is a complex number, then (bar(z^-1))(bar(z)) =

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

Find the conjugate of the complex number z= frac{(1+i)(2+i)}{(3+i)}

The complex number z satisfying the equation abs(frac{z-12}{z-8i})=frac{5}{3}, abs(frac{z-4}{z-8}) = 1

If z_1, z_2, z_3 are complex numbers such that abs(z_1)= abs(z_2) = abs(z_3) = abs(frac{1}{z_1}+frac{1}{z_2}+frac{1}{z_3}) = 1 , then abs(z_1+z_2+z_3) is

If z^2+z+1= 0 where z is a complex number, then the value of (z+frac{1}{z})^2+(z^2+frac{1}{z^2})^2+(z^3+frac{1}{z^3})^2 equals

The congugate of a complex number z is frac{1}{i-1} ,then the complex number is

If z_1 and z_2 are two non-zero complex numbers such that abs(z_1+z_2) = abs(z_1)+abs(z_2) , then arg(z_1)-arg(z_2) is equal to

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