How do you evaluate # 2 e^( ( 3 pi)/8 i) - 5 e^( ( 19 pi)/8 i)# using trigonometric functions?

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Answer 1 · 2018-04-26T11:59:33

#:. 2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i) ~~-1.15 -2.77 i #

#2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i)#

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

#(3 pi)/8 ~~ 1.178097 , (19 pi)/8 ~~ 7.461823#

#:. 2 e^((3 pi)/8i) = 2(cos ((3 pi)/8)+ i sin ((3 pi)/8))#

# =0.765367+ 1.847759 i #

#:. 5 e^((19 pi)/8 i) = 5(cos ((19 pi)/8)+ i sin ((19 pi)/8))#

# ~~ 1.913417 + 4.619397 i#

#:. 2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i) #

#=(0.765367+ 1.847759 i)- (1.913417 + 4.619397 i)#

#=( -1.148050- 2.771638 i)#

#:. 2 e^((3 pi)/8 i)- 5 e^((19 pi)/8 i) ~~-1.15 -2.77 i (2 dp)# [Ans]