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 z bar w= 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.

For complex numbers z and w prove that absz^2w-abs(w)^2z=z-w if and only if z=w or zbarw=1

The complex number z is is such that |z| =1, z ne -1 and w= (z-1)/(z+1). Then real part of w is-

The complex number z is such that |z|=1 , z ne -1 and w=(z-1)/(z+1) . Then real part of w is

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

Let z and w be two nonzero complex numbers such that |z|=|w| and arg(z)+a r g(w)=pidot Then prove that z=- barw dot