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受欢迎的代数 >

展开 (3+5i)^4

解答

展开

(3 + 5 i)^{4}

解答

- 644 - 960 i

求解步骤

(3 + 5 i)^{4}

使用二项式定理:

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

a = 3, b = 5 i

= i = 0 \sum 4 (i 4) \cdot 3^{(4 - i)} (5 i)^{i}

展开求和

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 3^{4} (5 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 3^{3} (5 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 3^{2} (5 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 3^{1} (5 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 3^{0} (5 i)^{4}

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 3^{4} (5 i)^{0} : 81

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 3^{3} (5 i)^{1} : 540 i

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 3^{2} (5 i)^{2} : 1350 i^{2}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 3^{1} (5 i)^{3} : 1500 i^{3}

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 3^{0} (5 i)^{4} : 625 i^{4}

= 81 + 540 i + 1350 i^{2} + 1500 i^{3} + 625 i^{4}

化简

81 + 540 i + 1350 i^{2} + 1500 i^{3} + 625 i^{4} : - 960 i - 644

= - 960 i - 644

Rewrite in standard complex form:

- 644 - 960 i

= - 644 - 960 i

流行的例子

展开 (1-5/p)^3

e x p an d (1 - \frac{5}{p})^{3}

展开-e(-e-e^2)

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

展开-(20s)/((s^2+25)^2)

e x p an d - \frac{20 s}{( s ^{2} + 25 ) ^{2}}

展开-sec(x)(2sin(2x)-tan(x)cos(2x))

e x p an d - sec (x) (2 sin (2 x) - tan (x) cos (2 x))

展开 ((x^2+1)(x^4-x^2+1))/(x^3)

e x p an d \frac{( x ^{2} + 1 ) ( x ^{4} - x ^{2} + 1 )}{x ^{3}}