How do you evaluate e^( ( 15 pi)/8 i) - e^( ( 11 pi)/12 i)e15π8i−e11π12i using trigonometric functions?

1 Answer
sankarankalyanam
Jul 17, 2018

color(magenta)(e^((15 pi)/(8) i) - e^(( 11pi)/12 i) ~~ -0.042 + -0.1239 ie15π8i−e11π12i≈−0.042+−0.1239i

Explanation:

e^((15 pi)/(8) i) - e^(( 11pi)/12 i)e15π8i−e11π12i

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

:. e^((15 pi)/(8) i) = (cos (15 pi)/(8)+ i (sin 15 pi)/(8))

= 0.9239 - 0.3827 i , IV Quadrant

:. e^(( 11pi)/12 i) = (cos ((11pi)/12)+ i sin ((11pi)/12))

~~ -0.9659 + 0.2588 i, II Quadrant

:. e^((15 pi)/(8) i) - e^(( 11pi)/12 i)

~~( 0.9239 - 0.3827 i ) - ( -0.9659 + 0.2588 i)

color(magenta)(e^((15 pi)/(8) i) - e^(( 11pi)/12 i) ~~ -0.042 + -0.1239 i

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