Let the roots of $x^n −1 = 0$ be $\alpha_1,\alpha_2,\cdots,\alpha_n$. Find the value of $(1−\alpha_1)(1−\alpha_2)\cdots(1−\alpha_n)$ in terms of $n$.
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Hint: $(1 - x)^n - 1$ has roots $1 - \alpha_i$. – Theo Bendit Mar 30 '24 at 05:39
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Hint: $1=\alpha_i$ for some $i$. But please provide more steps so that we can help you. – Angae MT Mar 30 '24 at 05:40
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so 0, is that simply all? – Soren Lorensen Mar 30 '24 at 05:42
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Do you miss some conditions like $\alpha_i\ne1$? – Angae MT Mar 30 '24 at 05:43
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no conditions given @Angae MT – Soren Lorensen Mar 30 '24 at 05:44
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Then that's all. Next time you should indicate your level of study so that we can discuss with the best language with you – Angae MT Mar 30 '24 at 05:45
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https://math.stackexchange.com/questions/1909362/product-of-one-minus-the-tenth-roots-of-unity – lab bhattacharjee Mar 30 '24 at 06:56
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It doesn't matter what the roots are, if a monic polynomial $p(x)$ has roots $\alpha_i$, then $(1-\alpha_1)(1-\alpha_2)\cdots(1-\alpha_n) =p(1)$. – Macavity Mar 30 '24 at 08:06