How do you multiply $e^{\frac{17 π}{12}} \cdot e^{\frac{π}{4} i}$ $e^((17 pi )/ 12 ) * e^( pi/4 i )$ in trigonometric form?

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Answer 1 · 2018-07-27T14:41:55

$\Rightarrow 60.5825 - 60.5825 i$ $color(purple)(=> 60.5825 - 60.5825 i)$

$e^{\frac{17 π}{12}} \cdot e^{(\frac{π}{4}) i}$ $e^((17pi)/12) * e^((pi/4)i)$

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

$\Rightarrow \frac{1}{\sqrt{2}} + (\frac{1}{\sqrt{2}}) i$ $=> 1/sqrt2 + (1/sqrt2) i$

$e^{\frac{17 π}{12}} \approx 85.6774$ $e^((17pi)/12) ~~ 85.6774$

$e^{\frac{17 π}{12}} \cdot e^{(\frac{π}{4}) i} = 85.6774 \cdot (0.7071 - 0.7071 i)$ $e^((17pi)/12) * e^((pi/4)i) = 85.6774 * (0.7071 - 0.7071 i)$

$\Rightarrow 60.5825 - 60.5825 i$ $color(purple)(=> 60.5825 - 60.5825 i)$

How do you multiply e^((17 pi )/ 12 ) * e^( pi/4 i ) e17π12⋅eπ4ie^((17 pi )/ 12 ) * e^( pi/4 i ) in trigonometric form?