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    Applying DeMoivre's Theorem

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    De Moivre's theorem states that

    (cos theta - i sin theta)^n = cos n theta + i sin n theta for n E R.

    (a) Use induction to prove de Moivre's theorem for n E Z^+.

    (b) Show that

    cos 5 theta = 16 cos^5 theta - 20 cos^3 theta + 5 cos theta.

    (c) Hence show that 2 cos pi/10 is a root of the equation

    x^4 - 5x^2 + 5 = 0.

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    https://brainmass.com/math/complex-analysis/applying-demoivre-s-theorem-188012

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    This solution illustrates how DeMoivre's theorem is applied to verifying the root of an equation. All calculations and steps are shown in the attached Word document which is attached.

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