Applications of de Moivre's Theorem (Edexcel A-Level Further Mathematics): Quizzes

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Applications of de Moivre's Theorem
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What does de Moivre's Theorem state for (cosθ+isinθ)n(cos \theta + i \sin \theta)^n?

cos(nθ)+isin(nθ)\cos(n \theta) + i \sin(n \theta)

Using de Moivre's Theorem with n=2n=2, what is cos(2θ)\cos(2\theta) equal to?

cos2θsin2θ\cos^2 \theta - \sin^2 \theta

Using de Moivre's Theorem with n=2n=2, what is sin(2θ)\sin(2\theta) equal to?

2cosθsinθ2 \cos \theta \sin \theta

What are the solutions to (cosθ+isinθ)3=1(\cos \theta + i \sin \theta)^3 = 1 for θ\theta in [0,2π)[0, 2\pi)?

0,2π3,4π30, \frac{2\pi}{3}, \frac{4\pi}{3}

What are the 4th roots of 16?

2,2i,2,2i2, 2i, -2, -2i

What is cos(3θ)\cos(3\theta) using the triple-angle formula?

cos3θ3cosθsin2θ\cos^3 \theta - 3 \cos \theta \sin^2 \theta

What is sin(3θ)\sin(3\theta) using the triple-angle formula?

3cos2θsinθsin3θ3 \cos^2 \theta \sin \theta - \sin^3 \theta

What is Euler's formula as used in summing trigonometric sequences?

eiθ=cosθ+isinθe^{i\theta} = \cos \theta + i \sin \theta

What type of series is 1+eiθ+ei2θ++einθ1 + e^{i\theta} + e^{i2\theta} + \dots + e^{in\theta}?

Geometric series

Which is NOT stated as an application of de Moivre's Theorem?

Finding derivatives of trig functions

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