vereinfachen (x+i-ix^2)^2

Lösung

vereinfachen

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

(- x^{4} + 3 x^{2} - 1) + (2 x - 2 x^{3}) i

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Setze Klammern

= xx + x i + x (- i x^{2}) + i x + ii + i (- i x^{2}) - i x^{2} x - i x^{2} i - i x^{2} (- i x^{2})

Vereinfache

xx + x i + x (- i x^{2}) + i x + ii + i (- i x^{2}) - i x^{2} x - i x^{2} i - i x^{2} (- i x^{2}) : - x^{4} + 3 x^{2} + 2 x i - 2 x^{3} i - 1

= - x^{4} + 3 x^{2} + 2 x i - 2 x^{3} i - 1

Rewrite in standard complex form:

(- x^{4} + 3 x^{2} - 1) + (2 x - 2 x^{3}) i

= (- x^{4} + 3 x^{2} - 1) + (2 x - 2 x^{3}) i

e x p an d \frac{2 s ^{2} + 67}{( s ^{2} + 1 ) ( s + 8 )}

e x p an d (x - \frac{5}{4}) (x - \frac{5}{4})

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

e x p an d (0, - 5) (x - 1)

e x p an d \frac{s ^{2} + s - 10 + e ^{- s}}{( s - 1 ) ( s - 2 ) ( s + 4 )}