All the roots of (z+1)4=z4 lie on

TIP It is unnecessary to find roots of (z+1)4=z4If z is a root of (z+1)4=z4, then (z+1)4=z4⇒|z+1|=|z|⇒|z−(−1)|=|z−0|⇒z lies on the perpendicular bisector of the segment join ing −1+0i and 0 i.e. z z lies on the line Re⁡(z)=−1/2.