If alpha and beta are the roots of the e...

If `alpha` and `beta` are the roots of the equation `x^2-2x+4=0`, prove that `alpha^n+beta^n=2^(n+1)cos(npi/3)`

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`x^2-2x+4=0`
`(x-1)^2+3=0`
`(x-1)^2=-3`
`(x-1)=pmsqrt3i`
`x=pmsqrt3i+1`
`x=2(1/2pmsqrt3/2i)`
`x-2(cospi/3pmisinpi/3)`
`x=2e^(pmipi/3)`
...

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