How do you evaluate $e^{\frac{19 π}{12} i} - e^{\frac{3 π}{4} i}$ $e^( ( 19 pi)/12 i) - e^( (3 pi)/4 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{19 π}{12} i} - e^{\frac{3 π}{4} i}$ $e^( ( 19 pi)/12 i) - e^( (3 pi)/4 i)$ using trigonometric functions?

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Answer 1 · 2016-04-09T13:20:58

$0.363 + 0.686 i$ $0.363 + 0.686i$

Explanation:

According to Euler's formula,

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

Substituting the different values for $x$ $x$ in the question,

$e^{\frac{19 π}{12} i} = cos (\frac{19 π}{12}) + i sin (\frac{19 π}{12})$ $e^((19pi)/12i) = cos((19pi)/12) + isin((19pi)/12)$
$= cos 285 + i sin 285$ $= cos285 + isin285$
$= - 0.633 + 0.774 i$ $= - 0.633 + 0.774i$

$e^{\frac{3 π}{4} i} = cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4})$ $e^((3pi)/4i) = cos((3pi)/4) + isin((3pi)/4)$
$= cos 135 + i sin 135$ $= cos135 + isin135$
$= - 0.996 + 0.088 i$ $= - 0.996 + 0.088i$

Using these values, the final answer is

$e^{\frac{19 π}{12} i} - e^{\frac{3 π}{4} i} ` = - 0.633 + 0.774 i + 0.996 - 0.088 i$ $e^((19pi)/12i) - e^((3pi)/4i) `= - 0.633 + 0.774i + 0.996 - 0.088i$
$= 0.363 + 0.686 i$ $= 0.363 + 0.686i$

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How do you evaluate $e^{\frac{19 π}{12} i} - e^{\frac{3 π}{4} i}$ $e^( ( 19 pi)/12 i) - e^( (3 pi)/4 i)$ using trigonometric functions?

1 Answer

Explanation:

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How do you evaluate $e^{\frac{19 π}{12} i} - e^{\frac{3 π}{4} i}$ $e^( ( 19 pi)/12 i) - e^( (3 pi)/4 i)$ using trigonometric functions?