Edexcel FP2 Official 2016 Exam Thread - 8th June 2016

[br]e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + ... + \frac{x^n}{n!}[br][br]x = i\theta[br][br]e^i^\theta = 1 + i\theta + \frac{(i\theta)^2}{2!} + \frac{(i\theta)^3}{3!} + ... + \frac{(i\theta)^n}{n!}[br][br]e^i^\theta = 1 +i\theta + \frac{i^2 \theta^2}{2!} + \frac{i^3 \theta^3}{3!} + ... + \frac{i^n \theta^n}{n!}[br][br]e^i^\theta = 1 +i\theta - \frac{\theta^2}{2!} - \frac{i \theta^3}{3!} + \frac{\theta^4}{4!} + ...[br][br]e^i^\theta = (1 - \frac{\theta^2}{2!} + \frac{\theta^4}{4!} + ...) + i(\theta - \frac{\theta^3}{3!} + \frac{\theta^5}{5!} + ...)[br][br](Using expansions for \cos\theta, \sin\theta)[br][br]e^i^\theta = \cos\theta + i\sin\theta[br][br]If z = r(\cos\theta + i\sin\theta), z = re^i^\theta[br][br]