Pentagram

Algebra Level 4

If \(z_1 , z_2 , z_3 , z_4 \) are the roots of the equation \( z^4 + z^3 + z^2 + z^1 + 1 = 0\), then what is the value of \(\displaystyle\sum_{i=1}^4 z_i ^5 \)?

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