vereinfachen (e^{iθ}-e^{-iθ})^5

Lösung

vereinfachen

(e^{i θ} - e^{- i θ})^{5}

32 i sin^{5} (θ)

Schritte zur Lösung

(e^{i θ} - e^{- i θ})^{5}

e^{i θ} = cos (θ) + i sin (θ)

e^{- i θ} = cos (θ) - i sin (θ)

= (cos (θ) + i sin (θ) - (cos (θ) - i sin (θ)))^{5}

Multipliziere aus

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

= (2 i sin (θ))^{5}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{5} i^{5} sin^{5} (θ)

2^{5} = 32

= 32 i^{5} sin^{5} (θ)

i^{5} = i

= 32 i sin^{5} (θ)

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

e x p an d \frac{( x - 4 ) ( x - 5 )}{( x - 3 ) ^{2} ( x + 1 ) ^{2}}

e x p an d \frac{2 ( 4 + x ) + e ^{- 3 x} ( 2 - x )}{( 2 - x ) ( 2 + x ) ( 4 x )}

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

e x p an d \frac{( ( 2 x - 1 ) ^{3} ( 26 - 6 x ) )}{( 4 - x ) ^{3}}