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If \( 1, \alpha_{1}, \alpha_{2}, \alpha_{3} \) and \( \alpha_{4} \) are the roots of \( x^{5}-1=0 \), then prove that
\( \mathrm{P} \) \( \frac{\omega-\alpha_{1}}{\omega^{2}-\alpha_{1}} \cdot \frac{\omega-\alpha_{2}}{\omega^{2}-\alpha_{2}} \cdot \frac{\omega-\alpha_{3}}{\omega^{2}-\alpha_{3}} \cdot \frac{\omega-\alpha_{4}}{\omega^{2}-\alpha_{4}}=\omega \), where \( \omega \) is

W a non-real complex root of unity.
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