簡約 (7+i/n)^2

解

簡約

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

\frac{49 n ^{2} - 1}{n ^{2}} + \frac{14}{n} i

解答ステップ

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

完全平方式を適用する:

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

(7 + \frac{i}{n})^{2} = 7^{2} + 2 \cdot 7 \cdot \frac{i}{n} + (\frac{i}{n})^{2}

= 7^{2} + 2 \cdot 7 \cdot \frac{i}{n} + (\frac{i}{n})^{2}

7^{2} = 49

2 \cdot 7 \cdot \frac{i}{n} = 14 \cdot \frac{i}{n}

(\frac{i}{n})^{2} = - \frac{1}{n ^{2}}

= 49 + 14 \cdot \frac{i}{n} - \frac{1}{n ^{2}}

簡素化

49 + 14 \cdot \frac{i}{n} - \frac{1}{n ^{2}} : \frac{49 n ^{2} - 1}{n ^{2}} + \frac{14}{n} i

= \frac{49 n ^{2} - 1}{n ^{2}} + \frac{14}{n} i