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Polar and Euler forms on an Argand diagram

Polar and Euler forms on an Argand diagram

IB Year 6 | Grade 12

Represent each of the following on an Argand diagram and express them in polar and Euler form.

  1. \(-2\)
  2. \(3i\)
  3. \(1+i\)
  4. \(-\sqrt{3}+i\)

Solution:

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Answer:(a) \(2(\cos\pi+i\sin\pi)=2e^{i\pi}\) (b) \(3\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)=3e^{i\pi/2}\) (c) \(\sqrt2\left(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\right)=\sqrt2e^{i\pi/4}\) (d) \(2\left(\cos\frac{5\pi}{6}+i\sin\frac{5\pi}{6}\right)=2e^{i5\pi/6}\)

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