How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?

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Answer 1 · 2018-07-27T14:30:21

$\Rightarrow - 0.1173 - 0.0579 i$ $color(maroon)(=> -0.1173 - 0.0579 i$ , III Quadrant.

Explanation:

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

$e^{(\frac{5 π}{3}) i} = cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})$ $e^(((5pi)/3) i )= cos ((5pi)/3) + i sin ((5pi)/3)$

$\approx > 0.5 - 0.866 i$ $~~> 0.5 - 0.866 i$ , IV Quadrant

$e^{(\frac{13 π}{8}) i} = cos (\frac{13 π}{8}) + i sin (\frac{13 π}{8})$ $e^(((13pi)/8)i) = cos ((13pi)/8) + i sin ((13pi)/8)$

$\Rightarrow 0.3827 - 0.9239 i$ $=> 0.3827 - 0.9239 i$ , IV Quadrant.

$e^{(\frac{π}{12}) i} - e^{(\frac{π}{8}) i} = - 0.3827 - 0.9239 i - 0.5 + 0.866 i$ $e^(((pi)/12)i) - e^(((pi)/8)i) = -0.3827 - 0.9239 i - 0.5 + 0.866 i$

$\Rightarrow - 0.1173 - 0.0579 i$ $color(chocolate)(=> -0.1173 - 0.0579 i$ , III Quadrant.

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{3} i}$ $e^( ( 13 pi)/8 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?