vereinfachen 1/2 (e^{-it}-e^{it})

Lösung

vereinfachen

\frac{1}{2} (e^{- i t} - e^{i t})

- i sin (t)

Schritte zur Lösung

\frac{1}{2} (e^{- i t} - e^{i t})

e^{- i t} = cos (t) - i sin (t)

e^{i t} = cos (t) + i sin (t)

= \frac{1}{2} (cos (t) - i sin (t) - (cos (t) + i sin (t)))

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( cos ( t ) - i sin ( t ) - ( cos ( t ) + sin ( t ) i ) )}{2}

1 \cdot (cos (t) - i sin (t) - (cos (t) + sin (t) i)) = cos (t) - i sin (t) - (cos (t) + i sin (t))

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

Multipliziere aus

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

= \frac{- 2 i sin ( t )}{2}

Wende Bruchregel an:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 i sin ( t )}{2}

Teile die Zahlen:

\frac{2}{2} = 1

= - i sin (t)

e x p an d - \frac{2 ( x ^{2} + x + 1 )}{( x ^{2} - 1 ) ^{2}}

e x p an d \frac{( 180 - 45 x ) ( x - 4 )}{2}

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e x p an d (ln (x)) (x^{2} (3 ln (x) + 1))

e x p an d (6 a^{3} + 2 ab - 8 b e^{2}) (3 a - 2 b)