express ((1+sin alpha+i cos alpha)/(1+sin alpha-i cos alpha))^(n) in the form a+ib
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Simplifying, we get
1+cos(2π−θ)−isin(2π−θ)1+cos(2π−θ)+isin(2π−θ)
=2cos2(4π−2θ)−i2cos(4π−2θ)sin((4π−2θ)2cos2(4π−2θ)+i2cos(4π−2θ)sin((4π−2θ)
=cos(4π−2
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