How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{π}{8} i}$ $e^( ( pi)/12 i) - e^( ( pi)/8 i)$ using trigonometric functions?

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How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{π}{8} i}$ $e^( ( pi)/12 i) - e^( ( pi)/8 i)$ using trigonometric functions?

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Answer 1 · 2018-07-27T14:12:39

$\Rightarrow 0.042 - 0.1239$ $color(chocolate)(=> 0.042 - 0.1239$ , IV Quadrant

Explanation:

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

$e^{(\frac{π}{12}) i} = cos (\frac{π}{12} + i sin (\frac{π}{12})$ $e^(((pi)/12) i )= cos ((pi)/12 + i sin ((pi)/12)$

$\approx > 0.9659 + 0.2588 i$ $~~> 0.9659 + 0.2588 i$ , I Quadrant

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

$\Rightarrow 0.9239 + 0.3827 i$ $=> 0.9239 + 0.3827 i$ , I Quadrant.

$e^{(\frac{π}{12}) i} - e^{(\frac{π}{8}) i} = 0.9659 - 0.9239 + 0.2588 i - 0.3827$ $e^(((pi)/12)i) - e^(((pi)/8)i) = 0.9659 - 0.9239 + 0.2588 i - 0.3827$

$\Rightarrow 0.042 - 0.1239$ $color(chocolate)(=> 0.042 - 0.1239$ , IV Quadrant.

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How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{π}{8} i}$ $e^( ( pi)/12 i) - e^( ( pi)/8 i)$ using trigonometric functions?

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