Unity in Math

Algebra Level 4

If \( \omega^3 = 1\), where \(\omega \ne 1 \). And \( z_1 = 2\omega + 3\omega^2 , z_2 = 2\omega^2 + 3\omega , z_3 = 5 \).

Find the value of \(z_1^3 + z_2^3 + z_3^3 \).

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