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If for z as real or complex such that ...

If for z as real or complex such that
` (1+z^(2) + z^(4))^(8) = C_(0)+ C_(1) z^(2) +C_(2) z^(4) + …+ C_(16) z^(32)` ,
prove that
`C_(0) + C_(3) + C_(6) + C_(9) + C_(12) + C_(15)`
` + (C_(2) + C_(5) + C_(8) + C_(11) + C_(14))``omega`
` + (C_(1) + C_(4) + C_(7) + C_(10) + C_(16)) omega^(2) = 0 ` ,
where `omega` is a cube root of unity .

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