Write on the trigonometric form the following complex number: -3(Cos $π$ $pi$ /4 + isin $π$ $pi$ /4) ?

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Write on the trigonometric form the following complex number: -3(Cos $π$ $pi$ /4 + isin $π$ $pi$ /4) ?

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Answer 1 · 2018-02-02T21:31:37

see explanation.

Explanation:

Well, I think of $- 3 (cos (\frac{π}{4}) + i sin (\frac{π}{4}))$ $-3(cos(pi/4)+isin(pi/4))$ , or $- 3 c i s (\frac{π}{4})$ $-3cis(pi/4)$ , as trig form. An alternative uses Euler's formula,

$r \cdot e^{i θ} = 4 (cos (θ) + i sin (θ))$ $r*e^(itheta) = 4(cos(theta)+isin(theta))$ ,

so we can also write it as $- 3 e^{\frac{π}{4} i}$ $-3e^(pi/4i)$ .

We could also write it in rectangular, or standard, form:

Since $cos (\frac{π}{4}) = sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $cos(pi/4) =sin(pi/4) = sqrt(2)/2$ we have:

$- 3 (cos (\frac{π}{4}) + i sin (\frac{π}{4})) = - 3 (\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} i)$ $-3(cos(pi/4)+isin(pi/4)) = -3(sqrt(2)/2 + sqrt(2)/2i)$

$= - \frac{3 \sqrt{2}}{2} - \frac{3 \sqrt{2}}{2} i$ $=-(3sqrt(2))/2 -(3sqrt(2))/2i$

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Write on the trigonometric form the following complex number: -3(Cos $π$ $pi$ /4 + isin $π$ $pi$ /4) ?

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Explanation:

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Science

Math

Humanities

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Write on the trigonometric form the following complex number: -3(Cosπpi/4 + isinπpi/4) ?

1 Answer

Explanation:

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Write on the trigonometric form the following complex number: -3(Cos $π$ $pi$ /4 + isin $π$ $pi$ /4) ?