How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i}$ $e^( ( 7 pi)/4 i) - e^( ( 11 pi)/6 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i}$ $e^( ( 7 pi)/4 i) - e^( ( 11 pi)/6 i)$ using trigonometric functions?

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Answer 1 · 2016-03-23T15:49:15

$e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i} = - 0.159 - 0.207 i$ $e^((7pi)/4 i) -e^((11pi)/6 i) = -0.159-0.207i$

Explanation:

$e^{i θ} = cos θ + i sin θ$ $e^(itheta) = cos theta +i sin theta$

$e^{\frac{7 π}{4} i} = cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})$ $e^((7pi)/4 i) = cos ((7pi)/4)+isin((7pi)/4)$

$e^{\frac{11 π}{6} i} = cos (\frac{11 π}{6}) + i sin (\frac{11 π}{6})$ $e^((11pi)/6 i) = cos ((11pi)/6)+isin((11pi)/6)$

$e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i} = [cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})] - [cos (\frac{11 π}{6}) + i sin (\frac{11 π}{6})]$ $e^((7pi)/4 i) -e^((11pi)/6 i) =[cos ((7pi)/4)+isin((7pi)/4)]-[cos ((11pi)/6)+isin((11pi)/6)]$

$e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i} = [cos (\frac{7 π}{4}) - cos (\frac{11 π}{6})] + i [sin (\frac{7 π}{4}) - sin (\frac{11 π}{6})]$ $e^((7pi)/4 i) -e^((11pi)/6 i) =[cos ((7pi)/4)-cos ((11pi)/6)]+i[sin((7pi)/4)-sin((11pi)/6)]$

$e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i} = - 0.159 - 0.207 i$ $e^((7pi)/4 i) -e^((11pi)/6 i) = -0.159-0.207i$

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{11 π}{6} i}$ $e^( ( 7 pi)/4 i) - e^( ( 11 pi)/6 i)$ using trigonometric functions?

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