Complex Numbers – Further Maths Paper 1

Candidates should be able to:

  • understand de Moivre’s theorem, for a positive integral exponent, in terms of the geometrical effect of multiplication of complex numbers;
  • prove de Moivre’s theorem for a positive integral exponent;
  • use de Moivre’s theorem for positive integral exponent to express trigonometrical ratios of multiple angles in terms of powers of trigonometrical ratios of the fundamental angle;
  • use de Moivre’s theorem, for a positive or negative rational exponent:
    • in expressing powers of \(\sin \theta\) and \(\cos \theta\) in terms of multiple angles,
    • in the summation of series,
    • in finding and using the \(n\)th roots of unity.

Complex numbers – Further Maths Paper 1 Videos Part 1 – 16

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