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3 years ago

11

Use De Moivre’s Theorem to compute the following:

29%2B8isin%284%5Cpi%2F5%29%29%7D%20" id="TexFormula1" title="\sqrt[3]{(8cos(4 \pi /5)+8isin(4\pi/5))} " alt="\sqrt[3]{(8cos(4 \pi /5)+8isin(4\pi/5))} " align="absmiddle" class="latex-formula">

1 answer:

Kipish [7]3 years ago

6 0

Hello here is a solution :

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3 years ago

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0.2.0.4, 0.6, 0.8, 1....<br> Arithmetic or geometric

Basile [38]

Arithmetic sequences have a common difference between consecutive terms.

Geometric sequences have a common ratio between consecutive terms.

Let's compute the differences and ratios between consecutive terms:

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$0.4-0.2 = 0.2,\quad 0.6-0.4=0.2,\quad 0.8-0.6=0.2,\quad 1-0.8=0.2$

Ratios:

$\dfrac{0.4}{0.2}=2,\quad \dfrac{0.6}{0.4} = 1.5,\quad \dfrac{0.8}{0.6} = 1.33\ldots, \quad\dfrac{1}{0.8}=1.25$

So, as you can see, the differences between consecutive terms are constant, whereas ratios vary.

So, this is an arithmetic sequence.

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3 years ago