# Can they really be distinct?

Algebra Level 4

Let $$a$$, $$b$$, and $$c$$ be distinct complex numbers such that

$\frac { a }{ 1-b } =\frac { b }{ 1-c } =\frac { c }{ 1-a } = k$

where $$k$$ is a complex number.

Find the sum of all values of $$k$$.

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