化简 (2-(2i)/n)^2

解答

化简

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

\frac{4 n ^{2} - 4}{n ^{2}} - \frac{8}{n} i

求解步骤

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

使用完全平方公式:

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

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

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

化简

2^{2} - 2 \cdot 2 \cdot \frac{2 i}{n} + (\frac{2 i}{n})^{2} : \frac{4 n ^{2} - 4}{n ^{2}} - \frac{8}{n} i

= \frac{4 n ^{2} - 4}{n ^{2}} - \frac{8}{n} i

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