vereinfachen (a+ib)^3

Lösung

vereinfachen

(a + ib)^{3}

(a^{3} - 3 a b^{2}) + (3 a^{2} b - b^{3}) i

Schritte zur Lösung

(a + ib)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(a + ib)^{3} = a^{3} + 3 a^{2} ib + 3 a (ib)^{2} + (ib)^{3}

= a^{3} + 3 a^{2} ib + 3 a (ib)^{2} + (ib)^{3}

3 a^{2} ib = 3 a^{2} bi

3 a (ib)^{2} = - 3 a b^{2}

(ib)^{3} = - i b^{3}

= a^{3} + 3 a^{2} bi - 3 a b^{2} - i b^{3}

Rewrite in standard complex form:

(a^{3} - 3 a b^{2}) + (3 a^{2} b - b^{3}) i

= (a^{3} - 3 a b^{2}) + (3 a^{2} b - b^{3}) i

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

s im pl i f y (2 + 3 i)^{5}

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

e x p an d x^{\frac{1}{7}} (x + 8)

e x p an d (1 + tan (α) tan (β)) tan (α - β)