What is the trigonometric form of $8 e^{\frac{5 π}{12} i}$ $8 e^( ( 5 pi)/12 i )$ ?

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What is the trigonometric form of $8 e^{\frac{5 π}{12} i}$ $8 e^( ( 5 pi)/12 i )$ ?

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Answer 1 · 2016-03-22T19:56:40

$8 [cos (\frac{5 π}{12}) + i sin (\frac{5 π}{12})]$ $8 [cos((5pi)/12) + isin((5pi)/12) ]$

Explanation:

Using $Euler's identity$ $color(blue)" Euler's identity"$ which states :

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

here r = 8 and $θ = \frac{5 π}{12}$ $theta = (5pi)/12$

$\Rightarrow 8 e^{\frac{5 π}{12} i} = 8 [cos (\frac{5 π}{12}) + i sin (\frac{5 π}{12})]$ $rArr 8e^((5pi)/12 i) = 8 [cos((5pi)/12) + isin((5pi)/12) ]$

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What is the trigonometric form of $8 e^{\frac{5 π}{12} i}$ $8 e^( ( 5 pi)/12 i )$ ?

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What is the trigonometric form of $8 e^{\frac{5 π}{12} i}$ $8 e^( ( 5 pi)/12 i )$ ?