簡約 (8+i/n)^2

解

簡約

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

\frac{64 n ^{2} - 1}{n ^{2}} + \frac{16}{n} i

解答ステップ

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

完全平方式を適用する:

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

(8 + \frac{i}{n})^{2} = 8^{2} + 2 \cdot 8 \cdot \frac{i}{n} + (\frac{i}{n})^{2}

= 8^{2} + 2 \cdot 8 \cdot \frac{i}{n} + (\frac{i}{n})^{2}

簡素化

8^{2} + 2 \cdot 8 \cdot \frac{i}{n} + (\frac{i}{n})^{2} : \frac{64 n ^{2} - 1}{n ^{2}} + \frac{16}{n} i

= \frac{64 n ^{2} - 1}{n ^{2}} + \frac{16}{n} i