2022TrialShort answer

Q11 (d)

2 marks

Question

Using De Moivre’s Theorem, find the 3 cube roots of $-4\sqrt2+4i\sqrt2$ . Leave your answers in modulus/argument form.

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Solution

$-4\sqrt2+4i\sqrt2=8\operatorname{cis}\frac{3\pi}{4}$

$\sqrt[3]{-4\sqrt2+4i\sqrt2}=2\operatorname{cis}\frac{\pi}{4},\quad 2\operatorname{cis}\frac{11\pi}{12},\quad 2\operatorname{cis}\frac{-3\pi}{4}$

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Syllabus alignment

Complex Numbers

Solving equations with complex numbersUse De Moivre's theorem and solve equations and polynomial problems involving complex and conjugate roots.

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