How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{17 π}{12} i}$ $e^( (3 pi)/2 i) - e^( ( 17 pi)/12 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{17 π}{12} i}$ $e^( (3 pi)/2 i) - e^( ( 17 pi)/12 i)$ using trigonometric functions?

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Answer 1 · 2016-09-29T17:54:16

$cos (\frac{3 π}{2}) - cos (\frac{11 π}{12}) + i {sin (\frac{3 π}{2}) - sin (\frac{11 π}{12})}$ $cos((3pi)/2) - cos((11pi)/12) + i{sin((3pi)/2) - sin((11pi)/12)}$

Explanation:

Use Euler's equation:

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

on each term and then combine like terms.

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How do you evaluate $e^{\frac{3 π}{2} i} - e^{\frac{17 π}{12} i}$ $e^( (3 pi)/2 i) - e^( ( 17 pi)/12 i)$ using trigonometric functions?

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