Let $z_{1}$ be $p$th root of unity and $z_{2}$ be $(p-1)$th root of unity then what is the absolute value of $\sum_{i=1}^{p-1}(z_1)^{j}(z_2)^{j}$.
I tried goemetric sum but stuck. Also this should be $\sqrt(p)$
$p$ is an odd prime.
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$\begingroup$ Is $p$ a prime? $\endgroup$– Parcly TaxelCommented Mar 29 at 5:31
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$\begingroup$ Yes i have edited thanks $\endgroup$– Mathslover shahCommented Mar 29 at 5:50
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1$\begingroup$ How did the geometric sum not work? $\endgroup$– Greg MartinCommented Mar 29 at 7:42
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$\begingroup$ Absolute value of $\frac{1- x^{p-1}}{1-x}$ $\endgroup$– Mathslover shahCommented Mar 29 at 9:34
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$\begingroup$ can you first double-check your sum and second specify which roots of unity you use as the answer seem to depend on that geometrically $\endgroup$– ConradCommented Mar 30 at 13:57
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