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

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

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Answer 1 · 2016-05-19T07:59:44

$e^{\frac{19 π}{12}} - e^{\frac{π}{4}} = - 0.4483 - i 1.673$ $e^((19pi)/12)-e^(pi/4)=-0.4483-i1.673$

Explanation:

$e^{\frac{19 π}{12} i} = cos (\frac{19 π}{12}) + i sin (\frac{19 π}{12})$ $e^((19pi)/12i)=cos((19pi)/12)+isin((19pi)/12)$ and $e^{\frac{π}{4} i} = cos (\frac{π}{4}) + i sin (\frac{π}{4})$ $e^(pi/4i)=cos(pi/4)+isin(pi/4)$

Hence, $e^{\frac{19 π}{12}} - e^{\frac{π}{4}} = cos (\frac{19 π}{12}) + i sin (\frac{19 π}{12}) - cos (\frac{π}{4}) - i sin (\frac{π}{4})$ $e^((19pi)/12)-e^(pi/4)=cos((19pi)/12)+isin((19pi)/12)-cos(pi/4)-isin(pi/4)$

= $cos (\frac{- 5 π}{12}) - cos (\frac{π}{4}) + i (sin (\frac{- 5 π}{12}) - sin (\frac{π}{4}))$ $cos((-5pi)/12)-cos(pi/4)+i(sin((-5pi)/12)-sin(pi/4))$

= $cos (\frac{5 π}{12}) - \frac{1}{\sqrt{2}} + i (- sin (\frac{5 π}{12}) - \frac{1}{\sqrt{2}})$ $cos((5pi)/12)-1/sqrt2+i(-sin((5pi)/12)-1/sqrt2)$

= $0.2588 - 0.7071 + i (- 0.9659 - 0.7071)$ $0.2588-0.7071+i(-0.9659-0.7071)$

= $- 0.4483 - i 1.673$ $-0.4483-i1.673$

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

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Explanation:

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