How do you evaluate # 2 e^( ( 3 pi)/8 i) - 3e^( ( 7 pi)/8 i)# using trigonometric functions?

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Answer 1 · 2018-06-07T11:59:10

#:2 e^((3 pi)/8 i)- 3 e^((7 pi)/8 i)~~( 3.54+0.70 i)#

#2 e^((3 pi)/8 i)- 3 e^((7 pi)/8 i)#

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

#(3 pi)/8 ~~ 1.178097 , (7 pi)/8 ~~ 2.748893#

#:. 2 e^((3 pi)/8i) = 2(cos ((3 pi)/8)+ i sin ((7 pi)/8))#

# =0.765367+ 1.847759 i #

#:. 3 e^((7 pi)/8 i) = 3(cos ((7 pi)/8)+ i sin ((7 pi)/8))#

# ~~ -2.77164 + 1.14805 i#

#:.2 e^((3 pi)/8 i)- 3 e^((7 pi)/8 i)#

#~~(0.765367+ 1.847759 i)- ( -2.77164 + 1.14805 i)#

#~~( 3.54+0.70 i) (2 dp)# [Ans]