Question

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

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

Step-by-step 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