How do you evaluate #e^( ( 3 pi)/8 i) - e^( ( 7 pi)/4 i)# using trigonometric functions?

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Answer 1 · 2018-05-30T10:40:26

#e^((3 pi)/8 i)-e^((7 pi)/4 i) ~~ -0.324 + 0.217 i#

#e^((3 pi)/8 i) - e^((7 pi)/4 i) = ?#

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

#(3 pi)/8 =(3*180)/8= 67.5^0 , (7 pi)/4= (7*180)/4 = 315.0^0#

#cos 67.5 ~~0.383 ; sin 67.5 = 0.924 ; cos 315 ~~ 0.707 ; #

#sin 315.0 ~~ -0.707 #

#e^((3 pi)/8 i)= cos 67.5 + sin 67.5*i=0.383 + 0.924 i #

#e^((7 pi)/4 i) = cos 315 + sin 315*i=0.707 - 0.707 i #

#e^((3 pi)/8 i)-e^((7 pi)/4 i)~~(0.383 + 0.924 i)-(0.707 - 0.707 i)#

or #e^((3 pi)/8 i)-e^((7 pi)/4 i) ~~ -0.324 + 0.217 i# [Ans[