How do you multiply $e^{\frac{5 π}{12}} \cdot e^{π i}$ $e^((5pi )/ 12 ) * e^( pi i )$ in trigonometric form?

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Answer 1 · 2018-07-05T21:31:29

$- e^{\frac{5 π}{12}}$ $-e^{{5\pi}/12}$

Using Euler's formula $e^{i θ} = cos θ + i sin θ$ $e^{i\theta}=\cos\theta+i\sin\theta$ as follows

$e^{\frac{5 π}{12}} \cdot e^{π i}$ $e^{{5\pi}/12}\cdot e^{\pi i}$

$= e^{\frac{5 π}{12}} (cos π + i sin π)$ $=e^{{5\pi}/12}(\cos \pi+i\sin\pi)$

$= e^{\frac{5 π}{12}} (- 1 + i 0)$ $=e^{{5\pi}/12}(-1+i0)$

$= - e^{\frac{5 π}{12}}$ $=-e^{{5\pi}/12}$

How do you multiply e5π12⋅eπie^((5pi )/ 12 ) * e^( pi i ) in trigonometric form?