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# How do you evaluate  e^( ( 13 pi)/8 i) - e^( (7 pi)/3 i) using trigonometric functions?

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#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

1
jim p. Share
Oct 16, 2017

Use Euler's formula...

#### Explanation:

...which is:

${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$

...so you'd have:

$\cos \left(\frac{13 \pi}{8}\right) + i \sin \left(\frac{13 \pi}{8}\right) - \left(\cos \left(\frac{7 \pi}{3}\right) + i \sin \left(\frac{7 \pi}{3}\right)\right)$

$0.383 - 0.924 i - 0.5 - 0.866 i$

$= - 0.117 - 0.058 i$

GOOD LUCK

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