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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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    Solution Summary

    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.