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受欢迎的代数 >

化简 (1+sqrt(3)*i)^4

解答

化简

(1 + 3 \cdot i)^{4}

解答

- 8 - 83 i

求解步骤

(1 + 3 i)^{4}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = 3 i

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (3 i)^{i}

展开求和

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (3 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (3 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (3 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (3 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (3 i)^{4}

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (3 i)^{0} : 1

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (3 i)^{1} : 43 i

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (3 i)^{2} : 18 i^{2}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (3 i)^{3} : 123 i^{3}

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (3 i)^{4} : 9 i^{4}

= 1 + 43 i + 18 i^{2} + 123 i^{3} + 9 i^{4}

化简

1 + 43 i + 18 i^{2} + 123 i^{3} + 9 i^{4} : - 83 i - 8

= - 83 i - 8

Rewrite in standard complex form:

- 8 - 83 i

= - 8 - 83 i

流行的例子

展开 9/(4x(5x+3))

e x p an d \frac{9}{4 x ( 5 x + 3 )}

展开 (2(x+1)(x-1))/(x+3)

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

展开 (7x-4)e^{4x}

e x p an d (7 x - 4) e^{4 x}

展开 (x^2-4)e^x

e x p an d (x^{2} - 4) e^{x}

d/(dv)((p)(p+(8.2)/(v^2))(v-5.4))

\frac{d}{d v} ((p) (p + \frac{8.2}{v ^{2}}) (v - 5.4))