How do you multiply $e^(( 5 pi )/ 3 i) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2018-07-17T09:38:31

$color(magenta)(e^((5 pi)/(3) i) * e^(( pi)/2 i)~~ 0.866 + 0.5 i$

$e^((5 pi)/(3) i) * e^(( pi)/2 i)$

$e^(i theta) = cos theta +i sin theta$

$:. e^((5 pi)/(3) i) = (cos (5 pi)/(3)+ i (sin 5 pi)/())$

$= 0.5 - 0.866 i$ , IV Quadrant

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

$= 0 + i$ , II Quadrant

$:. e^((5 pi)/(3) i) * e^(( pi)/2 i)$

$~~( 0.5 - 0.866 i ) - ( 0 + i)$

$color(magenta)(e^((5 pi)/(3) i) * e^(( pi)/2 i)~~ 0.866 + 0.5 i$

How do you multiply e^(( 5 pi )/ 3 i) * e^( pi/2 i ) e^(( 5 pi )/ 3 i) * e^( pi/2 i ) in trigonometric form?