zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

化简 (6+8i)^8

解答

化简

(6 + 8 i)^{8}

解答

42197248 + 90660864 i

求解步骤

(6 + 8 i)^{8}

使用二项式定理:

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

a = 6, b = 8 i

= i = 0 \sum 8 (i 8) \cdot 6^{(8 - i)} (8 i)^{i}

展开求和

= \frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 6^{8} (8 i)^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 6^{7} (8 i)^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 6^{6} (8 i)^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 6^{5} (8 i)^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 6^{4} (8 i)^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 6^{3} (8 i)^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 6^{2} (8 i)^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 6^{1} (8 i)^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 6^{0} (8 i)^{8}

化简

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 6^{8} (8 i)^{0} : 1679616

化简

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 6^{7} (8 i)^{1} : 17915904 i

化简

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 6^{6} (8 i)^{2} : 83607552 i^{2}

化简

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 6^{5} (8 i)^{3} : 222953472 i^{3}

化简

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 6^{4} (8 i)^{4} : 371589120 i^{4}

化简

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 6^{3} (8 i)^{5} : 396361728 i^{5}

化简

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 6^{2} (8 i)^{6} : 264241152 i^{6}

化简

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 6^{1} (8 i)^{7} : 100663296 i^{7}

化简

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 6^{0} (8 i)^{8} : 16777216 i^{8}

= 1679616 + 17915904 i + 83607552 i^{2} + 222953472 i^{3} + 371589120 i^{4} + 396361728 i^{5} + 264241152 i^{6} + 100663296 i^{7} + 16777216 i^{8}

化简

1679616 + 17915904 i + 83607552 i^{2} + 222953472 i^{3} + 371589120 i^{4} + 396361728 i^{5} + 264241152 i^{6} + 100663296 i^{7} + 16777216 i^{8} : 90660864 i + 42197248

= 90660864 i + 42197248

Rewrite in standard complex form:

42197248 + 90660864 i

= 42197248 + 90660864 i

流行的例子

化简 (1+i)^5+(1-i)^5

s im pl i f y (1 + i)^{5} + (1 - i)^{5}

展开 (1+e^{2x})^2

e x p an d (1 + e^{2 x})^{2}

展开 (5x-13)/((x-3)(x-2))

e x p an d \frac{5 x - 13}{( x - 3 ) ( x - 2 )}

展开 (1-sin(x))(sec(x)+tan(x))

e x p an d (1 - sin (x)) (sec (x) + tan (x))

展开 (sec(x)+tan(x))(1-sin(x))

e x p an d (sec (x) + tan (x)) (1 - sin (x))