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Conversion from polar to Cartesian form

Conversion from polar to Cartesian form

IB Year 6 | Grade 12

Express each of the following complex numbers in Cartesian form.

  1. \(4\left(\cos\dfrac{2\pi}{3}+i\sin\dfrac{2\pi}{3}\right)\)
  2. \(\sqrt{2}\left(\cos\left(-\dfrac{\pi}{4}\right)+i\sin\left(-\dfrac{\pi}{4}\right)\right)\)
  3. \(6\left(\cos\left(-\dfrac{5\pi}{6}\right)+i\sin\left(-\dfrac{5\pi}{6}\right)\right)\)

Solution:

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Answer:(a) \(-2+2\sqrt3\,i\) (b) \(1-i\) (c) \(-3\sqrt3-3i\)

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