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Integer power via De Moivre's Theorem

Integer power via De Moivre's Theorem

IB Year 6 | Grade 12

A complex number is given by \(z=-1+\sqrt{3}\,i\).

  1. Express \(z\) in polar form.
  2. Hence express \(z^5\) in Cartesian form.

Solution:

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Answer:(a) \(2\left(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\right)\) (b) \(-16-16\sqrt3\,i\)

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