How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{π}{2} i}$ $e^( ( 13 pi)/8 i) - e^( ( pi)/2 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{π}{2} i}$ $e^( ( 13 pi)/8 i) - e^( ( pi)/2 i)$ using trigonometric functions?

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Answer 1 · 2016-04-11T18:47:59

$e^{\frac{13 π}{8} i} - e^{\frac{π}{2} i} = 0.383 - 1.924 i$ $e^((13pi)/8i) - e^(pi/2i) = 0.383 - 1.924i$

Explanation:

According to Euler's formula,

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

Using values for $x$ $x$ from the equation, $\frac{13 π}{8}$ $(13pi)/8$ and $\frac{π}{2}$ $pi/2$

$x = \frac{13 π}{8}$ $x = (13pi)/8$
$e^{\frac{13 π}{8} i} = cos (\frac{13 π}{8}) + i sin (\frac{13 π}{8})$ $e^((13pi)/8i) = cos((13pi)/8) + isin((13pi)/8)$
$= cos 292.5 + i sin 292.5$ $= cos292.5 + isin292.5$
$= 0.383 - 0.924 i$ $= 0.383 - 0.924i$

$x = \frac{π}{2}$ $x = pi/2$
$e^{\frac{π}{2} i} = cos (\frac{π}{2}) + i sin (\frac{π}{2})$ $e^(pi/2i) = cos(pi/2) + isin(pi/2)$
$= cos 90 + i sin 90$ $= cos90 + isin90$
$= i$ $= i$

Inserting these two values back into the original question,

$e^{\frac{13 π}{8} i} - e^{\frac{π}{2} i} = 0.383 - 0.924 i - i$ $e^((13pi)/8i) - e^(pi/2i) = 0.383 - 0.924i - i$
$= 0.383 - 1.924 i$ $= 0.383 - 1.924i$

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{π}{2} i}$ $e^( ( 13 pi)/8 i) - e^( ( pi)/2 i)$ using trigonometric functions?

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Explanation:

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