 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2013/10/a/solution

De Moivre's theorem states that, for real

θ

n

(cos θ + i sin θ)^{n} = cos (n θ) + i sin (n θ) .

cos θ + i sin θ = e^{i θ}

and exponent multiplication. Negative integers are allowed because this unit-modulus complex number is nonzero. For a general polar number

r e^{i θ}

, its integer power also has the factor

r^{n}

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