Large powers can produce small results

Algebra Level 5

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

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