vereinfachen (5+3zi)^2

Lösung

vereinfachen

(5 + 3 z i)^{2}

(25 - 9 z^{2}) + 30 z i

Schritte zur Lösung

(5 + 3 z i)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(5 + 3 z i)^{2} = 5^{2} + 2 \cdot 5 \cdot 3 z i + (3 z i)^{2}

= 5^{2} + 2 \cdot 5 \cdot 3 z i + (3 z i)^{2}

5^{2} = 25

2 \cdot 5 \cdot 3 z i = 30 z i

(3 z i)^{2} = - 9 z^{2}

= 25 + 30 z i - 9 z^{2}

Rewrite in standard complex form:

(25 - 9 z^{2}) + 30 z i

= (25 - 9 z^{2}) + 30 z i

e x p an d \frac{3 x ^{3} + 10 x ^{2} + 27 x + 27}{x ^{2} ( x + 3 ) ^{2}}

e x p an d - x^{\frac{2}{3}} (x - 5)

s im pl i f y (x + 2 - 2) (x + 2 + 2)

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

s im pl i f y (\frac{x}{3} + \frac{y}{5}) (\frac{x}{3} - \frac{y}{5})