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Products and quotients of complex numbers

Question

Given that z1 = 5 + 3i and z2 = 2-2i. Determine the following in the form of r(cos x + sin x i).

  1. z1z2
  2. z1/z2
Answer

  1. √272(cos 0.921π + sin 0.921π i)
  2. √(34/8)(cos -0.579π + sin -0.579π i)
Note:

|z1z2| = r1r2, arg(z1z2) = y1 + y2

|z1/z2| = r1/r2, arg(z1/z2) = y1 – y2

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