By considering the binomial expansion of (z + 1/z)⁶, where z = cos θ + i sin θ, express cos⁶ θ in the form 1/32 (p + q cos 2θ + r cos 4θ + s cos 6θ), where p, q, r and s are integers to be determined.

By considering ∑_{r=1}^{n} z²ʳ⁻¹, where z = cos θ + i sin θ, show that, if sin θ ≠ 0, ∑_{r=1}^{n} sin (2r − 1)θ = sin…

Use de Moivre's theorem to express cot 7θ in terms of cot θ. Use the equation cot 7θ = 0 to show that the roots of th…

Let z = cos θ + i sin θ.

Let k and m be non-zero constants. The matrices A, B and C are given by A = [[0,1],[-1,1],[1,1]], B = [[k,0],[0,m]], …

The curve C has polar equation r² = tan 2θ, where 0 < θ < π/4.

The plane Π has equation x+3y+2z = 1. Relative to O, the points A, B, C have position vectors -j+2k, 2i-k, 2i-j-k, re…