vereinfachen (a+b*i)^3

Lösung

vereinfachen

(a + b \cdot i)^{3}

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

Schritte zur Lösung

(a + bi)^{3}

Wende Formel für perfekte dritte Potenzen an:

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

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

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

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

(bi)^{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

s im pl i f y (x - 1 - x^{2})^{2}

e x p an d 33 (539 - 4)

e x p an d \frac{2}{9} (3 k - 1)

s im pl i f y (4 x^{2} + x - \frac{3}{2}) (6 x - 8)

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