vereinfachen (3+(2i)/n)^2

Lösung

vereinfachen

(3 + \frac{2 i}{n})^{2}

\frac{9 n ^{2} - 4}{n ^{2}} + \frac{12}{n} i

Schritte zur Lösung

(3 + \frac{2 i}{n})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(3 + \frac{2 i}{n})^{2} = 3^{2} + 2 \cdot 3 \cdot \frac{2 i}{n} + (\frac{2 i}{n})^{2}

= 3^{2} + 2 \cdot 3 \cdot \frac{2 i}{n} + (\frac{2 i}{n})^{2}

3^{2} = 9

2 \cdot 3 \cdot \frac{2 i}{n} = 6 \cdot \frac{2 i}{n}

(\frac{2 i}{n})^{2} = - \frac{4}{n ^{2}}

= 9 + 6 \cdot \frac{2 i}{n} - \frac{4}{n ^{2}}

Vereinfache

9 + 6 \cdot \frac{2 i}{n} - \frac{4}{n ^{2}} : \frac{9 n ^{2} - 4}{n ^{2}} + \frac{12}{n} i

= \frac{9 n ^{2} - 4}{n ^{2}} + \frac{12}{n} i

s im pl i f y \frac{2 ( 2 3 + 3 )}{3}

e x p an d \frac{y ^{\frac{1}{3}}}{( y ^{\frac{4}{3}} - 9 ) ^{2}}

e x p an d \frac{aj + x}{( aj + c ) ( aj + b )}

e x p an d 3 sec (x) tan^{2} (x) + 3 (- sec (x) + 2 sec^{3} (x))

e x p an d (1 - \frac{z}{c})^{2}