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

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

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Answer 1 · 2016-04-09T17:32:03

$1.006 + 0.824 i$ $1.006 + 0.824i$

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,

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

$x = \frac{5 π}{3}$ $x = (5pi)/3$
$e^{\frac{5 π}{3} i} = cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})$ $e^((5pi)/3i) = cos((5pi)/3) + isin((5pi)/3)$
$= cos 300 + i sin 300$ $= cos300 + isin300$
$= - 0.022 - i$ $= - 0.022 - i$

Inserting these two values into the equation above,

$e^{\frac{3 π}{2} i} - e^{\frac{5 π}{3} i} = 0.984 - 0.176 i + 0.022 + i$ $e^((3pi)/2i) - e^((5pi)/3i) = 0.984 - 0.176i + 0.022 + i$
$= 1.006 + 0.824 i$ $= 1.006 + 0.824i$

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

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Explanation:

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