展開する 3(1+2/n i)^2

解

展開する

3 (1 + \frac{2}{n} i)^{2}

(3 - \frac{12}{n ^{2}}) + \frac{12}{n} i

解答ステップ

3 (1 + \frac{2}{n} i)^{2}

拡張

(1 + \frac{2}{n} i)^{2} : 1^{2} + 2 \cdot 1 \cdot \frac{2}{n} i + (\frac{2}{n} i)^{2}

= 3 (1^{2} + 2 \cdot 1 \cdot \frac{2}{n} i + (\frac{2}{n} i)^{2})

規則を適用する:

a \cdot 1 = a

= 3 (1^{2} + 2 \cdot \frac{2}{n} i + (\frac{2}{n} i)^{2})

分配法則を適用する:

m (a + b + c) = ma + mb + m c

3 (1^{2} + 2 \cdot \frac{2}{n} i + (\frac{2}{n} i)^{2}) = 3 \cdot 1^{2} + 3 \cdot 2 \cdot \frac{2}{n} i + 3 (\frac{2}{n} i)^{2}

= 3 \cdot 1^{2} + 3 \cdot 2 \cdot \frac{2}{n} i + 3 (\frac{2}{n} i)^{2}

簡素化

3 \cdot 1^{2} + 3 \cdot 2 \cdot \frac{2}{n} i + 3 (\frac{2}{n} i)^{2} : 3 + \frac{12}{n} i - \frac{12}{n ^{2}}

= 3 + \frac{12}{n} i - \frac{12}{n ^{2}}

標準的な複素数形式で書き直す:

(3 - \frac{12}{n ^{2}}) + \frac{12}{n} i

= (3 - \frac{12}{n ^{2}}) + \frac{12}{n} i