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#