How do you evaluate 2 e^( ( 23 pi)/8 i) - e^( ( 19 pi)/8 i)2e23π8i−e19π8i using trigonometric functions?

1 Answer
sankarankalyanam
Jul 17, 2018

color(maroon)(2e^((23 pi)/(8) i) - e^(( 19pi)/8 i) ~~ -2.2305 - 0.1585 i2e23π8i−e19π8i≈−2.2305−0.1585i

Explanation:

2e^((23 pi)/(8) i) - e^(( 19pi)/8 i)2e23π8i−e19π8i

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

:. 2e^((23 pi)/(8) i) = 2(cos ((23 pi)/8)+ i sin ((23 pi)/8))

= - 1.8478 + 0.7654 i , II Quadrant

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

0.3827 + 0.9239 i, I Quadrant

:. 2e^((23 pi)/(8) i) - e^(( 19pi)/8 i)

~~( -1.8478 + 0.7654 i ) - ( 0.3827 + 0.9239 i)

color(maroon)(2e^((23 pi)/(8) i) - e^(( 19pi)/8 i) ~~ -2.2305 - 0.1585 i

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