If 1, `alpha_(1), alpha_(2), alpha_(3),…….,alpha_(s)` are ninth roots of unity (taken in counter -clockwise sequence in the Argard plane). Then find the value of `|(2-alpha_(1))(2-alpha_(3)),(2-alpha_(5))(2-alpha_(7))`|.

Explanation

To solve the problem, we need to find the value of \( |(2 - \alpha_1)(2 - \alpha_3)(2 - \alpha_5)(2 - \alpha_7)| \), where \( \alpha_1, \alpha_2, \ldots, \alpha_8 \) are the ninth roots of unity.

### Step 1: Identify the ninth roots of unity
The ninth roots of unity are the solutions to the equation \( x^9 = 1 \). These can be expressed as:
\[ \alpha_k = e^{2\pi i k / 9} \quad \text{for } k = 0, 1, 2, \ldots, 8 \]
Thus, the ninth roots of unity are:
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