Reflections, scaling and addition of equal-modulus numbers

Reflections, scaling and addition of equal-modulus numbers

8 marks

The complex numbers \(z=4-3\mathrm{i}\) and \(w=-3+4\mathrm{i}\) have the same modulus. On a single Argand diagram, plot \(z\) and \(w\), and sketch the points representing

  1. \(z^*\),[2]
  2. \(-w\),[2]
  3. \(2w\),[2]
  4. \(z+w\).[2]

Label the coordinates of each point and show clearly the geometrical relationship of each result to \(z\) and \(w\).

Solution:

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Answer:(a) \(z^*=4+3\mathrm{i}\) (b) \(-w=3-4\mathrm{i}\) (c) \(2w=-6+8\mathrm{i}\) (d) \(z+w=1+\mathrm{i}\)

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