Show that the complex numbers z, satisfying the condition arg(`frac{z-1}{z+1}`) = (`pi`)/4 lies on a circle

The complex number z which satisfies the condition |frac{i+z}{i-z}| = 1 lies on.

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

The maximum value of abs(z) when z satisfies the condition abs(z-frac{2}{z}) = 2

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

The complex number frac{1+2i}{1-i} lies in the

If z=x+iy then abs(frac{z-1}{z+1}) =1 represents

Select and write the correct answer from the given alternatives in each of the following: If z is a complex number satisfying the relation |z + 1| = z + 2(1 +i), then z is

For any non zero complex number z, the minimum value of abs(z)+abs(z-1) is

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} )

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