If the roots of `(z-1)^n=i(z+1)^n` are plotted in ten Argand plane, then prove that they are collinear.

Explanation

We have `(z-1)^(n)=i(z+1)^(n)`
`:.|z-1|^(n)=|i||z+1|^(n)`
or `|z-1|^(n)=|z+1|^(n)`
or `|z-1|=|z+1|`
or `|z-1|^(2)=|z+1|^(2)`
`implies(x-1)^(2)+y^(2)=(x+1)^(2)+y^(2)`
or `4x=0" or "x=0.`
Therefore, the roots lies on the y-axis.