faktorisieren e^{j^{10}pit}-e^{-j^{10}pit}

Lösung

faktorisieren

e^{j^{10} π t} - e^{- j^{10} π t}

e^{- π j^{10} t} (e^{π j^{10} t} + 1) (e^{π j^{10} t} - 1)

Schritte zur Lösung

e^{j^{10} π t} - e^{- j^{10} π t}

Wende Exponentenregel an:

a^{b + c} = a^{b} a^{c}

e^{j^{10} t π} = e^{- j^{10} t π} e^{2 j^{10} t π}

= e^{- j^{10} t π} e^{2 j^{10} t π} - e^{- j^{10} t π}

Klammere gleiche Terme aus

e^{- j^{10} t π}

= e^{- j^{10} t π} (e^{2 j^{10} t π} - 1)

Faktorisiere

e^{2 π j^{10} t} - 1 : (e^{π j^{10} t} + 1) (e^{π j^{10} t} - 1)

= e^{- π j^{10} t} (e^{π j^{10} t} + 1) (e^{π j^{10} t} - 1)

f a c t or (x - 7) (3 x + 2) (x - 7) (3 x + 2)

f a c t or - a^{4} (2 h x)

f a c t or 3 \cdot (2 \cdot (- 5))

f a c t or 1 x^{2} - 2 x + 5

f a c t or (4^{3})^{2}