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Complex Roots Calculation

Let $ z $ be a complex number such that $ z^5 = 1 $ and $ z \neq 1 $. Compute \[z + \frac{1}{z} + z^2 + \frac{1}{z^2}.\]

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$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$