簡約 (3+(9i)/n)^2

解

簡約

(3 + \frac{9 i}{n})^{2}

\frac{9 n ^{2} - 81}{n ^{2}} + \frac{54}{n} i

解答ステップ

(3 + \frac{9 i}{n})^{2}

完全平方式を適用する:

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

(3 + \frac{9 i}{n})^{2} = 3^{2} + 2 \cdot 3 \cdot \frac{9 i}{n} + (\frac{9 i}{n})^{2}

= 3^{2} + 2 \cdot 3 \cdot \frac{9 i}{n} + (\frac{9 i}{n})^{2}

簡素化

3^{2} + 2 \cdot 3 \cdot \frac{9 i}{n} + (\frac{9 i}{n})^{2} : \frac{9 n ^{2} - 81}{n ^{2}} + \frac{54}{n} i

= \frac{9 n ^{2} - 81}{n ^{2}} + \frac{54}{n} i