How do you evaluate e^( ( 3 pi)/8 i) - e^( ( 7 pi)/4 i)e3π8i−e7π4i using trigonometric functions?

1 Answer
Binayaka C.
May 30, 2018

e^((3 pi)/8 i)-e^((7 pi)/4 i) ~~ -0.324 + 0.217 ie3π8i−e7π4i≈−0.324+0.217i

Explanation:

e^((3 pi)/8 i) - e^((7 pi)/4 i) = ?e3π8i−e7π4i=?

We know e^(itheta) = cos theta +i sin thetaeiθ=cosθ+isinθ

(3 pi)/8 =(3*180)/8= 67.5^0 , (7 pi)/4= (7*180)/4 = 315.0^03π8=3⋅1808=67.50,7π4=7⋅1804=315.00

cos 67.5 ~~0.383 ; sin 67.5 = 0.924 ; cos 315 ~~ 0.707 ; cos67.5≈0.383;sin67.5=0.924;cos315≈0.707;

sin 315.0 ~~ -0.707 sin315.0≈−0.707

e^((3 pi)/8 i)= cos 67.5 + sin 67.5*i=0.383 + 0.924 i e3π8i=cos67.5+sin67.5⋅i=0.383+0.924i

e^((7 pi)/4 i) = cos 315 + sin 315*i=0.707 - 0.707 i e7π4i=cos315+sin315⋅i=0.707−0.707i

e^((3 pi)/8 i)-e^((7 pi)/4 i)~~(0.383 + 0.924 i)-(0.707 - 0.707 i)e3π8i−e7π4i≈(0.383+0.924i)−(0.707−0.707i)

or e^((3 pi)/8 i)-e^((7 pi)/4 i) ~~ -0.324 + 0.217 ie3π8i−e7π4i≈−0.324+0.217i [Ans[

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