化简 (3+(i2)/n)^2

解答

化简

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

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

求解步骤

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

使用完全平方公式:

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

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

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

3^{2} = 9

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

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

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

化简

9 + 6 \cdot \frac{i 2}{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

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