If `z = x + iy,` then `1 <= |z| <= 3` represents

If z = x + iy where i = sqrt(-1) , then what does the equation zbarz +|z|^2 +4(z+barz)-48=0 represent?

If z = x + iy, z^(1//3) = a - ib , then x/a - y/b = ka^2 - b^2 , where k is equal to :

If z = x + iy and w=(1-iz)/(z-i) , show that : |w|=1 implies z is purely real.

If z=x+iy , then the equation |z+1|=|z-1| represents

If omega = sqrt(z^(2) - 1) where omega is a cube root of unity and z = x +iy then (1)/(2)[Tan^(-1) ((y)/(x + 1)) + Tan^(-1) ((y)/(x-1))]

If z = x - iy and z^(1/3)=p+iq, " then "(x/p+y/q)//(p^2+q^2)=