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Help with Complex Number Question (de Moivre's Theorem) (1 Viewer)

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The roots of the equation t²-2t+2=0 are a and b. Prove that [(x+a)ⁿ-(x+b)ⁿ]/(a-b) = (sin nθ)/(sinⁿ θ), where cot θ = x +1

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Q16slayer

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Assume, without loss of generality (because you can switch a and b and the expression would still be the same)
a = 1 + i
b = 1 - i
(worked out by quadratic formula)
x + 1 = cot theta
sub a, b, x+1 basically everything into LHS expression and simplify
 
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