How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{3 π}{2} i}$ $e^( ( 7 pi)/4 i) - e^( ( 3 pi)/2 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{3 π}{2} i}$ $e^( ( 7 pi)/4 i) - e^( ( 3 pi)/2 i)$ using trigonometric functions?

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Answer 1 · 2016-04-09T18:28:53

$- 0.317 + 0.921 i$ $- 0.317 + 0.921i$

Explanation:

According to Euler's theorem,

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

Therefore, using values for $x$ $x$ from the question,

$x = \frac{7 π}{4}$ $x = (7pi)/4$
$e^{\frac{7 π}{4} i} = cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})$ $e^((7pi)/4i) = cos((7pi)/4) + isin((7pi)/4)$
$= cos 315 + i sin 315$ $= cos315 + isin315$
$= 0.667 + 0.745 i$ $= 0.667 + 0.745i$

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

Put both these values back into the original question,

$e^{\frac{7 π}{4} i} - e^{\frac{3 π}{2} i} = 0.667 + 0.745 i - 0.984 + 0.176 i$ $e^((7pi)/4i) - e^((3pi)/2i) = 0.667 + 0.745i - 0.984 + 0.176i$
$= - 0.317 + 0.921 i$ $= - 0.317 + 0.921i$

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{3 π}{2} i}$ $e^( ( 7 pi)/4 i) - e^( ( 3 pi)/2 i)$ using trigonometric functions?

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Explanation:

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