Pentagram

Algebra Level 4

If z1,z2,z3,z4z_1 , z_2 , z_3 , z_4 are the roots of the equation z4+z3+z2+z1+1=0 z^4 + z^3 + z^2 + z^1 + 1 = 0, then what is the value of i=14zi5\displaystyle\sum_{i=1}^4 z_i ^5 ?

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