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Answer:
- complex plane; (cos(θ)+i·sin(θ))^n = cos(nθ) +i·sin(nθ)
- relationship between parameter and coordinates
- 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 ...
[tex](\cos(\theta)+i\sin(\theta))^n=\cos(n\theta)+i\sin(n\theta)[/tex]
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
