How can you use trigonometric functions to simplify $10 e^{\frac{4 π}{3} i}$ $10 e^( ( 4 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify $10 e^{\frac{4 π}{3} i}$ $10 e^( ( 4 pi)/3 i )$ into a non-exponential complex number?

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Answer 1 · 2016-03-03T12:10:35

$10 [cos (\frac{4 π}{3}) + i sin (\frac{4 π}{3})]$ $10[cos((4pi)/3) + isin((4pi)/3) ]$

Explanation:

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

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

here r = 10 and $θ = \frac{4 π}{3}$ $theta = (4pi)/3$

$\Rightarrow 10 e^{\frac{4 π}{3} i} = 10 [cos (\frac{4 π}{3}) + i sin (\frac{4 π}{3})]$ $rArr10e^((4pi)/3 i) = 10 [ cos( (4pi)/3) + isin((4pi)/3) ]$

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How can you use trigonometric functions to simplify $10 e^{\frac{4 π}{3} i}$ $10 e^( ( 4 pi)/3 i )$ into a non-exponential complex number?

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How can you use trigonometric functions to simplify 10e4π3i 10 e^( ( 4 pi)/3 i ) into a non-exponential complex number?

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How can you use trigonometric functions to simplify $10 e^{\frac{4 π}{3} i}$ $10 e^( ( 4 pi)/3 i )$ into a non-exponential complex number?