DeMoivre's Theorem (Leaving Cert Mathematics): Quizzes

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Using Demoivre to Prove Trigonometric Identities
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What can De Moivre's theorem be used to prove?

Trigonometric identities

What identity is proved using (cosθ+isin⁡θ)3(cos \theta + i \sin \theta)^3?

cos⁡(3θ)+isin⁡(3θ)\cos(3\theta) + i \sin(3\theta)

What is the first step when using De Moivre's theorem to prove an identity?

Expand the left-hand side

What technique is used after expanding (cosθ+isin⁡θ)3(cos \theta + i \sin \theta)^3?

Compare real with real, imaginary with imaginary

What is cos⁡(3θ)\cos(3\theta) equal to?

cos⁡3θ−3cos⁡θsin⁡2θ\cos^3 \theta - 3 \cos \theta \sin^2 \theta

What is sin⁡(3θ)\sin(3\theta) equal to?

3cos⁡2θsin⁡θ−sin⁡3θ3 \cos^2 \theta \sin \theta - \sin^3 \theta

What is the real part of (cosθ+isin⁡θ)3(cos \theta + i \sin \theta)^3 when expanded?

cos⁡3θ−3cos⁡θsin⁡2θ\cos^3 \theta - 3 \cos \theta \sin^2 \theta

What is the imaginary part of (cosθ+isin⁡θ)3(cos \theta + i \sin \theta)^3 when expanded?

3cos⁡2θsin⁡θ−sin⁡3θ3 \cos^2 \theta \sin \theta - \sin^3 \theta

Explore Leaving Cert Mathematics Revision Notes by Topics

Fundamentals of Complex Numbers

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Explore Leaving Cert Mathematics Model Answers by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

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Explore Leaving Cert Mathematics Flashcards by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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