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

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Answer 1 · 2018-07-17T09:53:55

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

# e^((23 pi)/(2) i) * e^(( pi)/2 i)#

#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#