How can you use trigonometric functions to simplify $27 e^{\frac{5 π}{3} i}$ $27 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $27 e^{\frac{5 π}{3} i}$ $27 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-07-19T22:20:40

You use Euler's Formula

Explanation:

Euler's Formula states that $e^{i θ} = cos (θ) + i sin (θ)$ $e^(itheta)=cos(theta)+isin(theta)$ Using trigonometry, you can readily see that $x = cos (θ) and y = sin (θ)$ $x=cos(theta) and y=sin(theta)$ . Hence, for your question, $27 e^{\frac{5 π}{3} i} = 27 (\frac{1}{2} - \frac{\sqrt{3}}{2} i)$ $27e^((5pi)/3i)=27(1/2-sqrt(3)/2i)$ .

Edit: Plugged in the wrong values originally. Now fixed.

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How can you use trigonometric functions to simplify $27 e^{\frac{5 π}{3} i}$ $27 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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Explanation:

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Science

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How can you use trigonometric functions to simplify 27e5π3i 27 e^( ( 5 pi)/3 i ) into a non-exponential complex number?

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Explanation:

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How can you use trigonometric functions to simplify $27 e^{\frac{5 π}{3} i}$ $27 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?