ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある代数 >

簡約 (1/(sqrt(2))+1/(sqrt(2))i)^{10}

解

簡約

(\frac{1}{2} + \frac{1}{2} i)^{10}

解

i

解答ステップ

(\frac{1}{2} + \frac{1}{2} i)^{10}

2項定理を適用する:

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

a = \frac{1}{2}, b = \frac{1}{2} i

= i = 0 \sum 10 (i 10) (\frac{1}{2})^{(10 - i)} (\frac{1}{2} i)^{i}

総和を展開する

= \frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{1}{2})^{10} (\frac{1}{2} i)^{0} + \frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{1}{2})^{9} (\frac{1}{2} i)^{1} + \frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{1}{2})^{8} (\frac{1}{2} i)^{2} + \frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{1}{2})^{7} (\frac{1}{2} i)^{3} + \frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{1}{2})^{6} (\frac{1}{2} i)^{4} + \frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{1}{2})^{5} (\frac{1}{2} i)^{5} + \frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{1}{2})^{4} (\frac{1}{2} i)^{6} + \frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{1}{2})^{3} (\frac{1}{2} i)^{7} + \frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{1}{2})^{2} (\frac{1}{2} i)^{8} + \frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{1}{2})^{1} (\frac{1}{2} i)^{9} + \frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{1}{2})^{0} (\frac{1}{2} i)^{10}

簡素化

\frac{10 !}{0 ! ( 10 - 0 ) !} (\frac{1}{2})^{10} (\frac{1}{2} i)^{0} : \frac{1}{32}

簡素化

\frac{10 !}{1 ! ( 10 - 1 ) !} (\frac{1}{2})^{9} (\frac{1}{2} i)^{1} : \frac{5 i}{16}

簡素化

\frac{10 !}{2 ! ( 10 - 2 ) !} (\frac{1}{2})^{8} (\frac{1}{2} i)^{2} : \frac{45 i ^{2}}{32}

簡素化

\frac{10 !}{3 ! ( 10 - 3 ) !} (\frac{1}{2})^{7} (\frac{1}{2} i)^{3} : \frac{15 i ^{3}}{4}

簡素化

\frac{10 !}{4 ! ( 10 - 4 ) !} (\frac{1}{2})^{6} (\frac{1}{2} i)^{4} : \frac{105 i ^{4}}{16}

簡素化

\frac{10 !}{5 ! ( 10 - 5 ) !} (\frac{1}{2})^{5} (\frac{1}{2} i)^{5} : \frac{63 i ^{5}}{8}

簡素化

\frac{10 !}{6 ! ( 10 - 6 ) !} (\frac{1}{2})^{4} (\frac{1}{2} i)^{6} : \frac{105 i ^{6}}{16}

簡素化

\frac{10 !}{7 ! ( 10 - 7 ) !} (\frac{1}{2})^{3} (\frac{1}{2} i)^{7} : \frac{15 i ^{7}}{4}

簡素化

\frac{10 !}{8 ! ( 10 - 8 ) !} (\frac{1}{2})^{2} (\frac{1}{2} i)^{8} : \frac{45 i ^{8}}{32}

簡素化

\frac{10 !}{9 ! ( 10 - 9 ) !} (\frac{1}{2})^{1} (\frac{1}{2} i)^{9} : \frac{5 i ^{9}}{16}

簡素化

\frac{10 !}{10 ! ( 10 - 10 ) !} (\frac{1}{2})^{0} (\frac{1}{2} i)^{10} : \frac{i ^{10}}{32}

= \frac{1}{32} + \frac{5 i}{16} + \frac{45 i ^{2}}{32} + \frac{15 i ^{3}}{4} + \frac{105 i ^{4}}{16} + \frac{63 i ^{5}}{8} + \frac{105 i ^{6}}{16} + \frac{15 i ^{7}}{4} + \frac{45 i ^{8}}{32} + \frac{5 i ^{9}}{16} + \frac{i ^{10}}{32}

簡素化

\frac{1}{32} + \frac{5 i}{16} + \frac{45 i ^{2}}{32} + \frac{15 i ^{3}}{4} + \frac{105 i ^{4}}{16} + \frac{63 i ^{5}}{8} + \frac{105 i ^{6}}{16} + \frac{15 i ^{7}}{4} + \frac{45 i ^{8}}{32} + \frac{5 i ^{9}}{16} + \frac{i ^{10}}{32} : i

= i

人気の例

簡約 (4s)/((s^2-4)^2)+2/(s^2-4)

s im pl i f y \frac{4 s}{( s ^{2} - 4 ) ^{2}} + \frac{2}{s ^{2} - 4}

8 \frac{1}{4} + 3 \frac{5}{6}

簡約 (3x^3-x^2)(-2x)

s im pl i f y (3 x^{3} - x^{2}) (- 2 x)

s im pl i f y (a^{4})^{3}

簡約 sqrt(-9/4)

s im pl i f y - \frac{9}{4}