vereinfachen (e^{iθ}-e^{-iθ})^2

Lösung

vereinfachen

(e^{i θ} - e^{- i θ})^{2}

- 4 sin^{2} (θ)

Schritte zur Lösung

(e^{i θ} - e^{- i θ})^{2}

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)))^{2}

Multipliziere aus

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

= (2 i sin (θ))^{2}

Wende Exponentenregel an:

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

= 2^{2} i^{2} sin^{2} (θ)

2^{2} = 4

= 4 i^{2} sin^{2} (θ)

i^{2} = - 1

= 4 (- 1) sin^{2} (θ)

Fasse zusammen

= - 4 sin^{2} (θ)

s im pl i f y (x + 46) (x - 46)

s im pl i f y 4 (3 x^{\frac{2}{3}} 3 x - 2 (x + 1))

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

e x p an d x (2 sin (x) + x cos (x))

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