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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