Further MathematicsCode 9231
Complex numbers
What this topic asks you to be able to do
- understand de Moivre’s theorem for an integer exponent, positive or negative, through the geometric meaning of multiplying and dividing complex numbers
- prove de Moivre’s theorem when the exponent is a positive integer
- use de Moivre’s theorem, with a rational exponent that is positive or negative, to write multiple-angle trigonometrical ratios as powers of the trigonometrical ratios at the fundamental angle
- apply de Moivre’s theorem, with a rational exponent that is positive or negative, to write sin i and cos i raised to a power as expressions involving multiple angles
- apply de Moivre’s theorem, with a rational exponent that is either positive or negative, when summing series
- apply de Moivre’s theorem, with a positive or negative rational exponent, to locate and make use of the nth roots of unity