How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2016-03-23T03:00:12

$e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i} \approx 1.0898 - 1.631 i$ $e^((7pi)/4 i)-e^((5pi)/8 i) ~~1.0898-1.631i$

Explanation:

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

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

$e^{\frac{5 π}{8} i} = cos (\frac{5 π}{8}) + i sin (\frac{5 π}{8})$ $e^((5pi)/8 i) = cos ((5pi)/8) +i sin ((5pi)/8)$

$e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i} = [cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})] - [cos (\frac{5 π}{8}) + i sin (\frac{5 π}{8})]$ $e^((7pi)/4 i)-e^((5pi)/8 i)=[cos( (7pi)/4) +i sin( (7pi)/4)]-[cos ((5pi)/8) +i sin ((5pi)/8)]$

$e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i} = [cos (\frac{7 π}{4}) - cos (\frac{5 π}{8})] + i [sin (\frac{7 π}{4}) - sin (\frac{5 π}{8})]$ $e^((7pi)/4 i)-e^((5pi)/8 i) = [cos( (7pi)/4)-cos ((5pi)/8)]+i[sin( (7pi)/4)-sin ((5pi)/8)]$

$e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i} \approx 1.0898 - 1.631 i$ $e^((7pi)/4 i)-e^((5pi)/8 i) ~~1.0898-1.631i$

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How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{8} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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