How do you evaluate $e^{\frac{11 π}{6} i} - e^{\frac{π}{8} i}$ $e^( ( 11 pi)/6 i) - e^( ( pi)/8 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{11 π}{6} i} - e^{\frac{π}{8} i}$ $e^( ( 11 pi)/6 i) - e^( ( pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2016-04-08T21:36:35

$- 0.188 + 0.355 i$ $- 0.188 + 0.355i$

Explanation:

According to Euler's formula,

$e^{i x} = cos x + i sin x$ $e^(ix) = cosx + isinx$ .

If we substitute the two values, beginning with $\frac{11 π}{6}$ $(11pi)/6$ ,

$cos (\frac{11 π}{6}) + i sin (\frac{11 π}{6}) = cos 330 + i sin 330$ $cos((11pi)/6) + isin((11pi)/6) = cos330 + isin330$
$= - 0.991 - 0.132 i$ $= - 0.991 - 0.132i$

$x = \frac{π}{8}$ $x = pi/8$
$cos (\frac{π}{8}) + i sin (\frac{π}{8}) = cos 22.5 + i sin 22.5$ $cos(pi/8) + isin(pi/8) = cos22.5 + isin22.5$
$= - 0.873 - 0.487 i$ $= - 0.873 - 0.487i$

Putting the two together,

$e^{\frac{11 π}{6} i} - e^{(\frac{π}{8}) i} = - 0.991 + 0.873 - 0.132 i + 0.487 i$ $e^((11pi)/6i) - e^((pi/8)i) = - 0.991 + 0.873 - 0.132i + 0.487i$
$= - 0.118 + 0.355 i$ $= - 0.118 + 0.355i$

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How do you evaluate $e^{\frac{11 π}{6} i} - e^{\frac{π}{8} i}$ $e^( ( 11 pi)/6 i) - e^( ( pi)/8 i)$ using trigonometric functions?

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Explanation:

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How do you evaluate e^( ( 11 pi)/6 i) - e^( ( pi)/8 i)e11π6i−eπ8i e^( ( 11 pi)/6 i) - e^( ( pi)/8 i) using trigonometric functions?

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How do you evaluate $e^{\frac{11 π}{6} i} - e^{\frac{π}{8} i}$ $e^( ( 11 pi)/6 i) - e^( ( pi)/8 i)$ using trigonometric functions?