Large powers can produce small results

Algebra Level 4

If the roots of 8x210x+3=08x^2-10x+3=0 are α\alpha and β2\beta^2 where β2>12\beta^2>\frac{1}{2}, then find the equation whose roots are (α+iβ)100(\alpha+i\beta)^{100} and (αiβ)100(\alpha-i\beta)^{100}.

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