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All the roots of $(z + 1)^{4} = z^{4}$ lie on

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Correct option is B

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.

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All the roots of (z+1)4=z4 lie on

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All the roots of $(z + 1)^{4} = z^{4}$ lie on