vereinfachen (e^{iwt}-e^{-iwt})e^{-inwt}

Lösung

vereinfachen

(e^{i wt} - e^{- i wt}) e^{- in wt}

2 sin (wt) sin (n wt) + 2 i sin (wt) cos (n wt)

Schritte zur Lösung

(e^{i wt} - e^{- i wt}) e^{- in wt}

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

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

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

e^{- in wt} = cos (n wt) - i sin (n wt)

= (cos (wt) + i sin (wt) - (cos (wt) - i sin (wt))) (cos (n wt) - i sin (n wt))

Wende arithmetische Regel für komplexe Zahlen an:

(ai) (b + c i) = - a c + abi

a = 2 sin (wt), b = cos (wt n), c = - sin (wt n)

= - 2 sin (wt) (- sin (wt n)) + 2 sin (wt) cos (wt n) i

Vereinfache

- 2 sin (wt) (- sin (wt n)) : 2 sin (wt) sin (n wt)

= 2 sin (wt) sin (n wt) + 2 sin (wt) cos (wt n) i

e x p an d (72 - 3) (53 + 2)

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

e x p an d (e^{t} - 9)^{2}

e x p an d (- 9 sin (x) + 9 sin (9 x))^{2}

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