erweitern (2+6/n*i)^2

Lösung

erweitern

(2 + \frac{6}{n} \cdot i)^{2}

(4 - \frac{36}{n ^{2}}) + \frac{24}{n} i

Schritte zur Lösung

(2 + \frac{6}{n} i)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(2 + \frac{6}{n} i)^{2} = 2^{2} + 2 \cdot 2 \cdot \frac{6}{n} i + (\frac{6}{n} i)^{2}

= 2^{2} + 2 \cdot 2 \cdot \frac{6}{n} i + (\frac{6}{n} i)^{2}

Vereinfache

2^{2} + 2 \cdot 2 \cdot \frac{6}{n} i + (\frac{6}{n} i)^{2} : 4 + \frac{24}{n} i - \frac{36}{n ^{2}}

= 4 + \frac{24}{n} i - \frac{36}{n ^{2}}

Rewrite in standard complex form:

(4 - \frac{36}{n ^{2}}) + \frac{24}{n} i

= (4 - \frac{36}{n ^{2}}) + \frac{24}{n} i

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