How do you multiply $e^{\frac{13 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 13 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{13 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 13 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2018-05-01T08:52:29

Just do the conversion and then multiply as you did back in Algebra I:
$e^{\frac{13 π}{8} i} = cos (\frac{13 π}{8}) + i \cdot sin (\frac{13 π}{8})$ $e^((13pi)/8i)=cos((13pi)/8)+i*sin((13pi)/8)$
$e^{\frac{π}{2} i} = cos (\frac{π}{2}) + i \cdot sin (\frac{π}{2}) = i$ $e^(pi/2i)=cos (pi/2) + i*sin (pi/2)=i$

$(cos (\frac{13 π}{8}) + i \cdot sin (\frac{13 π}{8})) \cdot i = - sin (\frac{13 π}{8}) + cos (\frac{13 π}{8}) i$ $(cos((13pi)/8)+i*sin((13pi)/8))*i=-sin((13pi)/8)+cos((13pi)/8)i$

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How do you multiply $e^{\frac{13 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 13 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{13 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 13 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?