How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{5 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{5 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2016-10-01T17:08:37

${cos (\frac{π}{12}) - cos (\frac{5 π}{8})} + i {sin (\frac{π}{12}) - sin (\frac{5 π}{8})}$ ${cos(pi/12) - cos((5pi)/8)} + i{sin(pi/12) - sin((5pi)/8)}$

Explanation:

Use Euler's formula $e^{(θ) i} = cos (θ) + i sin (θ)$ $e^((theta)i) = cos(theta) + isin(theta)$ on both terms:

$e^{(\frac{π}{12}) i} - e^{(\frac{5 π}{8}) i} =$ $e^((pi/12)i) - e^(((5pi)/8)i) =$

${cos (\frac{π}{12}) - cos (\frac{5 π}{8})} + i {sin (\frac{π}{12}) - sin (\frac{5 π}{8})}$ ${cos(pi/12) - cos((5pi)/8)} + i{sin(pi/12) - sin((5pi)/8)}$

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How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{5 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?

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How do you evaluate eπ12i−e5π8ie^( ( pi)/12 i) - e^( ( 5 pi)/8 i) using trigonometric functions?

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How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{5 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 5 pi)/8 i)$ using trigonometric functions?