# Almost 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 $$\left | \displaystyle\sum_{i=1}^4 z_i ^4 \right |$$?

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