How do you multiply $e^{\frac{19 π}{12}} \cdot e^{\frac{π}{4} i}$ $e^((19 pi )/ 12 ) * e^( pi/4 i )$ in trigonometric form?

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How do you multiply $e^{\frac{19 π}{12}} \cdot e^{\frac{π}{4} i}$ $e^((19 pi )/ 12 ) * e^( pi/4 i )$ in trigonometric form?

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Answer 1 · 2018-05-01T04:35:59

$e^{\frac{19 π}{12} i} e^{\frac{π}{4} i}$ $e^{{19 pi}/12 i } e^{ pi/4 i}$ $= e^{i (\frac{19 π}{12} + \frac{π}{4})}$ $= e^{i ({19 pi}/12 + pi/4) }$ $= e^{i (- \frac{π}{6})}$ $= e^{i (-pi/6 )}$ $= \frac{\sqrt{3}}{2} - \frac{i}{2}$ $= \sqrt{3}/2 - i/2$

Explanation:

I'm betting both of those are meant to have a factor of $i$ $i$ .

$e^{\frac{19 π}{12} i} e^{\frac{π}{4} i}$ $e^{{19 pi}/12 i } e^{ pi/4 i}$

$= e^{i (\frac{19 π}{12} + \frac{π}{4})}$ $= e^{i ({19 pi}/12 + pi/4) }$

$= e^{i (\frac{19 π}{12} + \frac{3 π}{12})}$ $= e^{i ({19 pi}/12 + {3pi}/12) }$

$= e^{i (\frac{22 π}{12})}$ $= e^{i ({22 pi}/12 ) }$

$= e^{i (\frac{11 π}{6})}$ $= e^{i ({11 pi}/6 ) }$

$= e^{i (- \frac{π}{6})}$ $= e^{i (-pi/6 )}$

$= cos (\frac{π}{6}) - i sin (\frac{π}{6})$ $= cos (pi/6) - i sin (pi/6)$

$= \frac{\sqrt{3}}{2} - \frac{i}{2}$ $= \sqrt{3}/2 - i/2$

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How do you multiply $e^{\frac{19 π}{12}} \cdot e^{\frac{π}{4} i}$ $e^((19 pi )/ 12 ) * e^( pi/4 i )$ in trigonometric form?

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How do you multiply $e^{\frac{19 π}{12}} \cdot e^{\frac{π}{4} i}$ $e^((19 pi )/ 12 ) * e^( pi/4 i )$ in trigonometric form?