展开 3(1+2/n i)^2

解答

展开

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

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

求解步骤

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

展开

(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})

使用法则:

a \cdot 1 = a

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

使用分配律:

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}

化简

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}}

Rewrite in standard complex form:

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

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

e x p an d (n + 7) lo g_{7} (x)

s im pl i f y (\frac{x ^{3}}{2} + 4 x^{2} - \frac{7 x}{9}) (2 x + 5)

e x p an d - \frac{2}{s ^{3} ( s ^{2} + 1 )}

e x p an d \frac{cot ( x )}{sec ( x )}

e x p an d \frac{( s ^{2} + 1 )}{( s + 1 ) ^{3}}