No. 1!

Algebra Level 5

Let $$z$$ be a complex number satisfying:

$\color{Purple}{\huge{|z|=|z+1|=1}}$

Also,

$$\color{Green}{\huge{z^{n}=(z+1)^{n}}}$$ where $$\color{Blue}{n}$$ is a positive integer.

Find the minimum value of $$\color{Red}{n}$$.

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