How do you multiply $e^{\frac{23 π}{2}} \cdot e^{\frac{π}{2} i}$ $e^((23 pi )/ 2 ) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2018-07-17T09:53:55

$e^{\frac{23 π}{2} i} \cdot e^{\frac{π}{2} i} = - 1$ $color(crimson)(e^((23 pi)/(2) i) * e^(( pi)/2 i) = -1$

$e^{\frac{23 π}{2} i} \cdot e^{\frac{π}{2} i}$ $e^((23 pi)/(2) i) * e^(( pi)/2 i)$

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

$:. e^((23 pi)/(2) i) = (cos (23 pi)/(2)+ i (sin 23 pi)/(1))$

$= 0 - i$ , IV Quadrant

$:. e^(( pi)/2 i) = (cos ((pi)/2)+ i sin ((pi)/2))$

$= 0 + i$ , I Quadrant

$:. e^((23 pi)/(2) i) * e^(( pi)/2 i)$

$=( 0 - i ) - ( 0 + i)$

$color(crimson)(e^((23 pi)/(2) i) * e^(( pi)/2 i) = -1$

How do you multiply e^((23 pi )/ 2 ) * e^( pi/2 i ) e23π2⋅eπ2ie^((23 pi )/ 2 ) * e^( pi/2 i ) in trigonometric form?