For complex numbers `z and w`, prove that `|z|^2w- |w|^2 z = z - w`, if and only if `z = w` or `z barw = 1`.

For complex numbers z and w, prove that |z|^(2)w-|w|^(2)z=z-w, if and only if z=w or zbar(w)=1.

If complex variables z,w are such that w=(2z-7i)/(z+i) and |w|=2, then z lies on:

If omega is any complex number such that z omega = |z|^2 and |z - barz| + |omega + bar(omega)| = 4 then as omega varies, then the area bounded by the locus of z is

Which one of the following is correct? Ifz and w are complex numbers and overset(-)(w) denotes the conjugate of w, then |z+w|=|z-w| holds only, if