# 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