# Similar to Roots of Unity or Not?

Algebra Level pending

Let $$n$$ be even natural number. Suppose that $$r_1, r_2, ..., r_n$$ are all complex roots of $$x^n = -1$$. Find

$(ar_1 +1)(ar_2 +1)(ar_3 +1)...(ar_n +1) - a^n$

where $$a$$ is any real number.

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