How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{19 π}{12} i}$ $e^( (3 pi)/2 i) - e^( ( 19 pi)/12 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{19 π}{12} i}$ $e^( (3 pi)/2 i) - e^( ( 19 pi)/12 i)$ using trigonometric functions?

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Answer 1 · 2016-01-19T12:30:42

$- 0.25882 - 0.034 i$ $-0.25882-0.034i$

Explanation:

By Euler's Theorem, $e^{i θ} = cos θ + i sin θ$ $e^(itheta)=costheta+isintheta$ .

Applying this theorem to the given example yields

$cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2}) - (cos (\frac{19 π}{12}) + i sin (\frac{19 π}{12}))$ $cos((3pi)/2)+isin((3pi)/2)-(cos((19pi)/12)+isin((19pi)/12))$

$= (0 - i) - (0.25882 - 0.966 i)$ $=(0-i)-(0.25882-0.966i)$

$= - 0.25882 - 0.034 i$ $=-0.25882-0.034i$

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How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{19 π}{12} i}$ $e^( (3 pi)/2 i) - e^( ( 19 pi)/12 i)$ using trigonometric functions?

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