If `abs(z+1)` = z+2 (1+i), then find z

If abs(z^2-1) =(abs(z))^2+1 , then z lies on

If arg(z-1)=arg(z+3i), then find (x-1)/y, where z=x+iy

If abs(z_1+z_2) = abs(z_1-z_2) , then the difference in the amplitudes of z_1 and z_2 is

If abs(z_1) =1, ( z_1 != -1) and z_2 = frac{z_1 - 1}{z_1 +1} , then show that the real part of z_2 is zero.

If z=(-1-i) , then arg z =

If abs(z_1) = abs(z_2) , is it necessary that z_1 = z_2 ?

If abs(z-3+ i) = 4 then, the locus of z is

If z=x+iy and abs(z - zi) = 1, then,

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

If z_1 = 1-i and z_2 = 2+4i , then im[frac{z_1z_2}{z_1} =