How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{4} i}$ $e^( ( 13 pi)/8 i) - e^( (5 pi)/4 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{4} i}$ $e^( ( 13 pi)/8 i) - e^( (5 pi)/4 i)$ using trigonometric functions?

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Answer 1 · 2018-07-27T14:01:18

$e^{(\frac{13 π}{8}) i} - e^{(\frac{5 π}{4}) i} = - 0.3244 - 1.631$ $color(crimson)(e^(((13pi)/8)i) - e^(((5pi)/4)i) = -0.3244 - 1.631$ , III Quadrant.

Explanation:

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

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

$\approx > 0.3827 - 0.9239 i$ $~~> 0.3827 - 0.9239 i$ , IV Quadrant

$e^{(\frac{5 π}{4}) i} = cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4})$ $e^(((5pi)/4)i) = cos ((5pi)/4) + i sin ((5pi)/4)$

$\Rightarrow - 0.7071 - 0.7071 i$ $=> -0.7071 - 0.7071 i$ , III Quadrant.

$e^{(\frac{13 π}{8}) i} - e^{(\frac{5 π}{4}) i} = 0.3827 - 0.7071 - 0.9239 i - 0.7071 i$ $e^(((13pi)/8)i) - e^(((5pi)/4)i) = 0.3827 - 0.7071 - 0.9239i - 0.7071i$

$\Rightarrow - 0.3244 - 1.631$ $=> -0.3244 - 1.631$ , III Quadrant.

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How do you evaluate $e^{\frac{13 π}{8} i} - e^{\frac{5 π}{4} i}$ $e^( ( 13 pi)/8 i) - e^( (5 pi)/4 i)$ using trigonometric functions?

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Explanation:

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