If \( z \) is the imaginary \( 5^{\text {th }} \) root of unity, th...

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If \( z \) is the imaginary \( 5^{\text {th }} \) root of unity, then
\( \mathrm{P} \)
\[
\frac{z^{4}}{1+z^{4}}+\frac{z}{1+z}+\frac{z^{2}}{1+z^{2}}+\frac{z^{4}}{z+z^{4}}=
\]
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