Question

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE explain thoroughly. Chapter 16

1. What is De Movire's Theorem and what plane is it related to?

2. What information do you need to be able to graph a parametric equation?

3. What is the relationship between rectangle coordinates and polar coordinates?

Answer 1

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Answer:

1. complex plane; (cos(θ)+i·sin(θ))^n = cos(nθ) +i·sin(nθ)
2. relationship between parameter and coordinates
3. basically: (x, y) = (r·cos(θ), r·sin(θ)); can be solved for r, θ

Explanation:

1. de Moivre's theorem (or identity) states that ...

`(\cos(\theta)+i\sin(\theta))^n=\cos(n\theta)+i\sin(n\theta)`

It is a statement about powers of complex numbers, so is related to the complex plane.

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2. To graph a parametric equation, you need to know the relationship between the parameter and the coordinates you want to graph.

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3. Here are the relationships:

(x, y) = (r·cos(θ), r·sin(θ))

(r, θ) = (√(x² +y²), arctan(y/x)) . . . with attention to quadrant