How can you use trigonometric functions to simplify $8 e^{\frac{5 π}{3} i}$ $8 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $8 e^{\frac{5 π}{3} i}$ $8 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-02-26T09:56:44

$8 [cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})]$ $8[cos((5pi)/3) + isin((5pi)/3) ]$

Explanation:

using $Euler's relation, which states$ $color(blue) " Euler's relation" , " which states "$

$r e^{θ i} = r (cos θ + i sin θ)$ $re^(theta i) = r (costheta + isintheta )$

here r = 8 and $θ = \frac{5 π}{3}$ $theta = (5pi)/3$

$\Rightarrow 8 e^{\frac{5 π}{3} i} = 8 [cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})]$ $rArr8e^((5pi)/3 i) = 8 [ cos((5pi)/3) + isin((5pi)/3) ]$

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How can you use trigonometric functions to simplify $8 e^{\frac{5 π}{3} i}$ $8 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify 8e5π3i 8 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 $8 e^{\frac{5 π}{3} i}$ $8 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?