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Geometric interpretation of arithmetic operations

Geometric interpretation of arithmetic operations

IB Year 6 | Grade 12

Let \(z = x + yi\) and \(w = u + vi\) be two given complex numbers.

State, in terms of vectors, the interpretation of the following operations, i.e.,

  1. \(z + w\);
  2. \(z - w\);
  3. \(\lambda z\), where \(\lambda\) is a positive real number; and
  4. \(\mu z\), where \(\mu\) is a negative real number.

Solution:

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Answer:(a) \(\binom{x+u}{y+v}=\mathbf z+\mathbf w\) (b) \(\binom{x-u}{y-v}=\mathbf z-\mathbf w=\overrightarrow{WZ}\) (c) \(\lambda\mathbf z\): same direction, length multiplied by \(\lambda\) (d) \(\mu\mathbf z\): opposite direction, length multiplied by \(|\mu|\)

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