How do you multiply $e^{\frac{13 π}{12}} \cdot e^{\frac{π}{4} i}$ $e^((13 pi )/ 12 ) * e^( pi/4 i )$ in trigonometric form?

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Answer 1 · 2018-07-17T07:55:26

$e^{\frac{13 π}{12} i} \cdot e^{\frac{π}{4} i} \approx - 0.5 - 0.866 i$ $color(purple)(e^((13 pi)/(12) i) * e^(( pi)/4 i) ~~ -0.5 - 0.866 i$

$e^{\frac{13 π}{12} i} \cdot e^{\frac{π}{4} i}$ $e^((13 pi)/(12) i) * e^(( pi)/4 i)$

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

$\frac{3 π}{8} \approx 3.4034, \frac{π}{4} \approx 0.7854$ $(3 pi)/8 ~~ 3.4034 , ( pi)/4 ~~ 0.7854$

$:. e^((13 pi)/(12) i) = (cos ((13 pi)/12)+ i sin ((13 pi)/12))$

$= - 0.9659 - 0.2588 i$ , III Quadrant

$:. e^(( pi)/4 i) = (cos (pi/4)+ i sin (pi/4)$

$~~ 0.7071 + 0.7071 i$

$:. e^((13 pi)/(12) i) * e^(( pi)/4 i)$

$~~( - 0.9659 - 0.2588 i ) * ( 0.7071 + 0.7071 i)$

$~~ -0.683 + 0.183 -0 .683 i - 0.183 i$

$color(purple)(e^((13 pi)/(12) i) * e^(( pi)/4 i) ~~ -0.5 - 0.866 i$

How do you multiply e^((13 pi )/ 12 ) * e^( pi/4 i ) e13π12⋅eπ4ie^((13 pi )/ 12 ) * e^( pi/4 i ) in trigonometric form?