vereinfachen (e^{-iw}-1)^2(e^{iw}-1)^2

Lösung

vereinfachen

(e^{- i w} - 1)^{2} (e^{i w} - 1)^{2}

sin^{4} (w) + 2 sin^{2} (w) + 2 sin^{2} (w) cos^{2} (w) - 4 sin^{2} (w) cos (w) + cos^{4} (w) - 4 cos^{3} (w) + 6 cos^{2} (w) - 4 cos (w) + 1

Schritte zur Lösung

(e^{- i w} - 1)^{2} (e^{i w} - 1)^{2}

(e^{- i w} - 1)^{2} = (cos (w) - i sin (w) - 1)^{2}

= (cos (w) - i sin (w) - 1)^{2} (e^{i w} - 1)^{2}

(e^{i w} - 1)^{2} = (cos (w) + i sin (w) - 1)^{2}

= (cos (w) - i sin (w) - 1)^{2} (cos (w) + i sin (w) - 1)^{2}

= (cos (w) - i sin (w) - 1)^{2} (cos (w) + i sin (w) - 1)^{2}

(cos (w) - i sin (w) - 1)^{2} = (cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1)

= (cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1) (cos (w) + i sin (w) - 1)^{2}

(cos (w) + sin (w) i - 1)^{2} = (cos (w) + sin (w) i - 1) (cos (w) + sin (w) i - 1)

= (cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1) (cos (w) + i sin (w) - 1) (cos (w) + i sin (w) - 1)

Multipliziere aus

(cos (w) - i sin (w) - 1) (cos (w) - i sin (w) - 1) (cos (w) + sin (w) i - 1) (cos (w) + sin (w) i - 1) : sin^{4} (w) + 2 sin^{2} (w) + 2 sin^{2} (w) cos^{2} (w) - 4 sin^{2} (w) cos (w) + cos^{4} (w) - 4 cos^{3} (w) + 6 cos^{2} (w) - 4 cos (w) + 1

= sin^{4} (w) + 2 sin^{2} (w) + 2 sin^{2} (w) cos^{2} (w) - 4 sin^{2} (w) cos (w) + cos^{4} (w) - 4 cos^{3} (w) + 6 cos^{2} (w) - 4 cos (w) + 1

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

e x p an d 8 n - 6 (- 5 n - 3 = 18 + 7 n)

s im pl i f y e^{(- 2 + iπn) x}

e x p an d 1 + (3 x^{2})^{4}

e x p an d \frac{3 x + 79}{2 ( x - 3 ) ( x + 8 )}