How do you multiply e^((11pi )/ 12 ) * e^( pi i ) e11π12⋅eπi in trigonometric form?

1 Answer
Kalyanam S.
Jul 27, 2018

color(purple)(e^((11 pi)/(12) i) * e^(( pi) i) ~~ 0.9659 - 0.2588 ie11π12i⋅e(π)i≈0.9659−0.2588i, IV Quadrant.

Explanation:

e^((11 pi)/(12) i) * e^(( pi) i)e11π12i⋅e(π)i

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

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

= - 0.9659 + 0.2588 i , II Quadrant

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

= -1, II Quadrant.

:. e^((11 pi)/(12) i) * e^(( pi) i)

~~( - 0.9659 + 0.2588 i ) * ( -1 )

~~ 0.9659 - 0.2588 i

color(purple)(e^((11 pi)/(12) i) * e^(( pi) i) ~~ 0.9659 - 0.2588 i, IV Quadrant.

Verification :

=> e^i (((11pi)/12) + (pi))

=> e^i ((23pi)/12)

=> cos ((23pi)/12) + i sin ((23pi)/12)

=> 0.9659 - 0.2588i, IV Quadrant.

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