Maths with David

    9231. FP2. Complex Numbers. Past Exam Questions

    9231/21/M/J/25q1

    Find the roots of the equation z3 = 27 – 27i, giving your answers in the form re^{ i \theta } , where r>0 and - \pi \leq \theta < \pi . [5 marks]

    9231/21/M/J/25q3

    By considering the binomial expansion of ( z - \frac{1}{z} )^5 , where z = cos \theta + isin \theta , used de Moivre’s theorem to show that

    cosec^5 \theta = \frac{ a }{ sin 5 \theta + b sin 3 \theta + c sin \theta } ,

    where a, b and c are integers to be determined. [6 marks]