If `1,alpha,alpha^2,alpha^3,......,alpha^(n-1)`are `n` `n^(th)` roots of unity, then find the value of `(2011-alpha)(2011-alpha^2)....(2011-alpha^(n-1))`

Explanation

To solve the problem, we need to find the value of the expression \((2011 - \alpha)(2011 - \alpha^2) \ldots (2011 - \alpha^{n-1})\), where \(1, \alpha, \alpha^2, \ldots, \alpha^{n-1}\) are the \(n\)th roots of unity.

### Step-by-Step Solution:

1. **Understanding the Roots of Unity**:
The \(n\)th roots of unity are the solutions to the equation \(x^n = 1\). These roots can be expressed as:
\[
1, \alpha, \alpha^2, \ldots, \alpha^{n-1}
...