Operations on complex numbers in polar form

Lessons

• 1.
  Multiplying complex numbers in polar form
  
  a)

  $4(\cos(\frac{5\pi}{3})+i \sin(\frac{5\pi}{3})) \cdot 8(\cos(\frac{2\pi}{3})+i \sin(\frac{2\pi}{3}))$
  
  
  b)

  $(\cos(170^{\circ})+i \sin(170^{\circ}))\cdot 5(\cos(45^{\circ})+i \sin(45^{\circ}))$
  
  
  c)

  $3(\cos(\pi)+i \sin(\pi))\cdot(\cos(\frac{\pi}{5})+i \sin(\frac{\pi}{5}))\cdot6(\cos(\frac{2\pi}{3})+i \sin(\frac{2\pi}{3}))$
  
  

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• 2.
  Dividing complex numbers in polar form
  
  a)

  $20(\cos(\frac{5\pi}{2})+i \sin(\frac{5\pi}{2}))\div 6(\cos(\frac{2\pi}{3})+i \sin(\frac{2\pi}{3}))$
  
  
  b)

  $3(\cos(\frac{3\pi}{4})+i \sin(\frac{3\pi}{4}))\div 12(\cos(\frac{\pi}{6})+i \sin(\frac{\pi}{6}))$
  
  
  c)

  $(\cos(262^{\circ})+i \sin(262^{\circ}))\div (\cos(56^{\circ})+i \sin(56^{\circ}))$
  
  

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• 3.
  Convert the following complex number to exponential form
  $z=3+i$

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