What is (e^{4i}-e^{-4i})/(2i) ?

The solution to (e^{4i}-e^{-4i})/(2i) is sin(4)

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simplify (e^{4i}-e^{-4i})/(2i)

simplify

\frac{e ^{4 i} - e ^{- 4 i}}{2 i}

sin (4)

Decimal Notation

- 0.75680 \dots

Solution steps

\frac{e ^{4 i} - e ^{- 4 i}}{2 i}

e^{4 i} - e^{- 4 i} = cos (4) + i sin (4) - (cos (4) - i sin (4))

= \frac{cos ( 4 ) + i sin ( 4 ) - ( - i sin ( 4 ) + cos ( 4 ) )}{2 i}

Expand

cos (4) + sin (4) i - (cos (4) - sin (4) i) : 2 i sin (4)

= \frac{2 i sin ( 4 )}{2 i}

Divide the numbers:

\frac{2}{2} = 1

= \frac{i sin ( 4 )}{i}

Cancel the common factor:

i

= sin (4)

\frac{9}{4} + \frac{1}{2}

(5^{2})^{0}

e^{l n ∣ x ∣ + x}

\frac{e}{e}

(x^{2} - x + 4) (3 x^{2} + 3 x - 4)