vereinfachen (e^{ix}+e^{-ix})^2

Lösung

vereinfachen

(e^{i x} + e^{- i x})^{2}

4 cos^{2} (x)

Schritte zur Lösung

(e^{i x} + e^{- i x})^{2}

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

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

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

Vereinfache

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

= (2 cos (x))^{2}

Wende Exponentenregel an:

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

= 2^{2} cos^{2} (x)

2^{2} = 4

= 4 cos^{2} (x)

s im pl i f y (- 23 - 2 i)^{5}

e x p an d (x - x^{2}) (sin (x) + x^{2} - 15)

e x p an d (x - 5 - 2) (3 + x)

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

e x p an d \frac{2 x ^{3} - 6}{x ( x ^{2} + 3 x + 8 ) ( x ^{2} + x + 1 )}