Let a complex number \( \alpha, \alpha \neq 1 \), be a root of the ...

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Let a complex number \( \alpha, \alpha \neq 1 \), be a root of the equation
\[
z^{p+q}-z^{p}-z^{q}+1=0
\]
\( \mathrm{P} \) where, \( p \) and \( q \) are distinct primes. Show that either

W or \( \quad 1+\alpha+\alpha^{2}+\ldots+\alpha^{q-1}=0 \) but not both together.
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