Complex zeros of the polynomial function.?

F(z)=1 - z^2 + z^4 (z^2 + 1) f(z) = (1 + z^6) z^6 = (-1) the "roots of unity" z^6 = (cos 2k+1 pi + I sin 2k+1 pi) z = (cos (2k+1) pi + I sin (2k+1) pi)^1/6 z = (cos (2k+1)/6 pi + I sin (2k+1)/6 pi) z = sqrt 3/2 + 1/2 I z = 0 + I z = -sqrt 3/2 + 1/2 I z = -sqrt 3/2 - 1/2 I z = 0 - I z = sqrt 3/2 - 1/2 I but....those are the roots of (z^2 + 1) f(z) and i, and -i are roots of (z^2 + 1) and not roots of f(z) z = sqrt 3/2 + 1/2 I z = -sqrt 3/2 + 1/2 I z = -sqrt 3/2 - 1/2 I z = sqrt 3/2 - 1/2 i.

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