What is ((e^{3i}-e^{-3i}))/(2i) ?

The solution to ((e^{3i}-e^{-3i}))/(2i) is sin(3)

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simplify ((e^{3i}-e^{-3i}))/(2i)

simplify

\frac{( e ^{3 i} - e ^{- 3 i} )}{2 i}

sin (3)

Decimal Notation

0.14112 \dots

Solution steps

\frac{e ^{3 i} - e ^{- 3 i}}{2 i}

e^{3 i} - e^{- 3 i} = cos (3) + i sin (3) - (cos (3) - i sin (3))

= \frac{cos ( 3 ) + i sin ( 3 ) - ( - i sin ( 3 ) + cos ( 3 ) )}{2 i}

Expand

cos (3) + sin (3) i - (cos (3) - sin (3) i) : 2 i sin (3)

= \frac{2 i sin ( 3 )}{2 i}

Divide the numbers:

\frac{2}{2} = 1

= \frac{i sin ( 3 )}{i}

Cancel the common factor:

i

= sin (3)

4 x + 6 - x = 2 x + 3

- 2 x^{3} - 4 x^{2} - 3 x - 6

- 6 p - 6

3 ∣ y ∣ + 7 > 1

28 = 14 + 2 x^{2}

What is ((e^{3i}-e^{-3i}))/(2i) ?
The solution to ((e^{3i}-e^{-3i}))/(2i) is sin(3)