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Question

Prove that the roots of (z1)n=i(z+1)n when plotted in the Argand plane are collinear.

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Solution

we have (z1)n=i(z+1)n
|z1|n=|i||z+1|n
or |z1|n=|z+1|n
or |z1|=|z+1|
or |z1|2=|z+1|2
(x1)2+y2=(x+1)2+y2
or 4x=0 or x=0
Therefore, the roots lie on the y-axis.

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