How can you use trigonometric functions to simplify $24 e^{\frac{5 π}{3} i}$ $24 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $24 e^{\frac{5 π}{3} i}$ $24 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-03-02T16:45:31

$24 [cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})]$ $24[ cos((5pi)/3) + isin((5pi)/3) ]$

Explanation:

Using $Euler's relationship$ $color(blue) " Euler's relationship "$

which states $r e^{θ i} = r [cos θ + i sin θ]$ $re^(thetai) = r[costheta + isintheta]$

here r = 24 and $θ = \frac{5 π}{3}$ $theta = (5pi)/3$

$\Rightarrow 24 e^{\frac{5 π}{3} i} = 24 [cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})]$ $rArr 24e^((5pi)/3 i) = 24 [ cos((5pi)/3) + isin((5pi)/3) ]$

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How can you use trigonometric functions to simplify $24 e^{\frac{5 π}{3} i}$ $24 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify 24 e^( ( 5 pi)/3 i ) 24e5π3i 24 e^( ( 5 pi)/3 i ) into a non-exponential complex number?

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How can you use trigonometric functions to simplify $24 e^{\frac{5 π}{3} i}$ $24 e^( ( 5 pi)/3 i )$ into a non-exponential complex number?