How do you evaluate # e^( (3 pi)/2 i) - e^( (15 pi)/8 i)# using trigonometric functions?

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Answer 1 · 2017-05-20T11:00:59

#e^((3pi)/2i) - e^((15pi)/8i) ~~ -0.924 - 0.617 i#

We know #e^(itheta) = cos theta +i sin theta#

#(3pi)/2 =(3*180)/2= 270^0 , (15 pi)/8= (15*180)/8 = 337.5^0#

#cos 270 =0 ; sin(270) = -1 ; cos 337.5 ~~ 0.924 ; #

#sin 337.5 ~~ -0.383 #

#:. e^((3pi)/2i) = cos ((3pi)/2)+ i sin ((3pi)/2) = 0 - i #

#:. e^((15pi)/8i) = cos ((15pi)/8)+ i sin ((15pi)/8) ~~ 0.924 - 0.383 i#

# :. e^((3pi)/2i) - e^((15pi)/8i) ~~ (0- i) - ( 0.924 - 0.383 i)# or

# ~~ (-0.924) + (-1+0.383)i ~~ -0.924 - 0.617 i# [Ans]