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Substituting the given values for b and c into the equation for abc,

a(-2 + 3i)(1 + 2i) = -37 + 36i

Multiplying out the terms in brackets...

De Moivre's Theorem states that if z = cos(q)+isin(q), then

zⁿ = (cos(q)+isin(q))ⁿ = cos(nq)+isin(nq)

But then 

z^-n = cos(-nq)...

At GCSE level, proof questions are relatively rare and largely will all require a similar sort of approach. The difference with A Level is that the syllabus contains more than one method of proof. You wil...

If you look at the Taylor series expansion of e^x: e^x = 1 + x + x²/(2!) + x³/(3!) + x⁴/(4!)...

If you then make this e^ix, ...

The easiest way of approaching this question is to use De Moivre's formula: e^(inx) = cos(nx) + isin(nx) from which it is simple to show that cos(nx) = (e^(inx) + e^(-inx)) / 2 and sin(nx) = (e^(inx))- e^...