How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{7 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( (7 pi)/3 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{7 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( (7 pi)/3 i)$ using trigonometric functions?

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Answer 1 · 2017-10-16T14:17:42

Use Euler's formula...

Explanation:

...which is:

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

...so you'd have:

$cos (\frac{13 π}{8}) + i sin (\frac{13 π}{8}) - (cos (\frac{7 π}{3}) + i sin (\frac{7 π}{3}))$ $cos((13pi)/8) + isin((13pi)/8) - (cos((7pi)/3) + isin((7pi)/3))$

So, make sure your calculator is in "radians" mode instead of degrees. You get:

$0.383 - 0.924 i - 0.5 - 0.866 i$ $0.383 -0.924i - 0.5 - 0.866i$

$= - 0.117 - 0.058 i$ $= -0.117 - 0.058i$

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{7 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( (7 pi)/3 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{7 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( (7 pi)/3 i)$ using trigonometric functions?