How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{5 π}{8} i}$ $e^( (3 pi)/2 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{5 π}{8} i}$ $e^( (3 pi)/2 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2016-04-08T22:22:18

$0.157 + 0.386 i$ $0.157 + 0.386i$

Explanation:

According to Euler's formula,

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

Inserting values for $x = \frac{3 π}{2}$ $x = (3pi)/2$ and $\frac{5 π}{8}$ $(5pi)/8$ ,

$e^{\frac{3 π}{2} i} = cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2})$ $e^((3pi)/2i) = cos((3pi)/2) + isin((3pi)/2)$
$= cos 270 + i sin 270$ $= cos270 + isin270$
$= 0.984 - 0.176 i$ $= 0.984 - 0.176i$

$e^{\frac{5 π}{8} i} = cos (\frac{5 π}{8}) + i sin (\frac{5 π}{8})$ $e^((5pi)/8i) = cos((5pi)/8) + isin((5pi)/8)$
$= cos 112.5 + i sin 112.5$ $= cos112.5 + isin112.5$
$= 0.827 - 0.562 i$ $= 0.827 - 0.562i$

Putting both of these together,

$e^{\frac{3 π}{2} i} - e^{\frac{5 π}{8} i} = 0.984 - 0.827 - 0.176 i + 0.562 i$ $e^((3pi)/2i) - e^((5pi)/8i) = 0.984 - 0.827 - 0.176i + 0.562i$
$= 0.157 + 0.386 i$ $= 0.157 + 0.386i$

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How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{5 π}{8} i}$ $e^( (3 pi)/2 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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Explanation:

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