it

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Algebra >

semplificare (sqrt(3)+i)^{11}

Soluzione

semplificare

(3 + i)^{11}

Soluzione

10243 - 1024 i

Fasi della soluzione

(3 + i)^{11}

Applicare il teorema binomiale:

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

a = 3, b = i

= i = 0 \sum 11 (i 11) (3)^{(11 - i)} i^{i}

Espandere la sommatoria

= \frac{11 !}{0 ! ( 11 - 0 ) !} (3)^{11} i^{0} + \frac{11 !}{1 ! ( 11 - 1 ) !} (3)^{10} i^{1} + \frac{11 !}{2 ! ( 11 - 2 ) !} (3)^{9} i^{2} + \frac{11 !}{3 ! ( 11 - 3 ) !} (3)^{8} i^{3} + \frac{11 !}{4 ! ( 11 - 4 ) !} (3)^{7} i^{4} + \frac{11 !}{5 ! ( 11 - 5 ) !} (3)^{6} i^{5} + \frac{11 !}{6 ! ( 11 - 6 ) !} (3)^{5} i^{6} + \frac{11 !}{7 ! ( 11 - 7 ) !} (3)^{4} i^{7} + \frac{11 !}{8 ! ( 11 - 8 ) !} (3)^{3} i^{8} + \frac{11 !}{9 ! ( 11 - 9 ) !} (3)^{2} i^{9} + \frac{11 !}{10 ! ( 11 - 10 ) !} (3)^{1} i^{10} + \frac{11 !}{11 ! ( 11 - 11 ) !} (3)^{0} i^{11}

Semplificare

\frac{11 !}{0 ! ( 11 - 0 ) !} (3)^{11} i^{0} : 2433

Semplificare

\frac{11 !}{1 ! ( 11 - 1 ) !} (3)^{10} i^{1} : 2673 i

Semplificare

\frac{11 !}{2 ! ( 11 - 2 ) !} (3)^{9} i^{2} : 44553 i^{2}

Semplificare

\frac{11 !}{3 ! ( 11 - 3 ) !} (3)^{8} i^{3} : 13365 i^{3}

Semplificare

\frac{11 !}{4 ! ( 11 - 4 ) !} (3)^{7} i^{4} : 89103 i^{4}

Semplificare

\frac{11 !}{5 ! ( 11 - 5 ) !} (3)^{6} i^{5} : 12474 i^{5}

Semplificare

\frac{11 !}{6 ! ( 11 - 6 ) !} (3)^{5} i^{6} : 41583 i^{6}

Semplificare

\frac{11 !}{7 ! ( 11 - 7 ) !} (3)^{4} i^{7} : 2970 i^{7}

Semplificare

\frac{11 !}{8 ! ( 11 - 8 ) !} (3)^{3} i^{8} : 4953 i^{8}

Semplificare

\frac{11 !}{9 ! ( 11 - 9 ) !} (3)^{2} i^{9} : 165 i^{9}

Semplificare

\frac{11 !}{10 ! ( 11 - 10 ) !} (3)^{1} i^{10} : 113 i^{10}

Semplificare

\frac{11 !}{11 ! ( 11 - 11 ) !} (3)^{0} i^{11} : i^{11}

= 2433 + 2673 i + 44553 i^{2} + 13365 i^{3} + 89103 i^{4} + 12474 i^{5} + 41583 i^{6} + 2970 i^{7} + 4953 i^{8} + 165 i^{9} + 113 i^{10} + i^{11}

Semplificare

2433 + 2673 i + 44553 i^{2} + 13365 i^{3} + 89103 i^{4} + 12474 i^{5} + 41583 i^{6} + 2970 i^{7} + 4953 i^{8} + 165 i^{9} + 113 i^{10} + i^{11} : - 1024 i + 10243

= - 1024 i + 10243

Riscrivi in forma complessa standard:

10243 - 1024 i

= 10243 - 1024 i

Esempi popolari

espandere (2(3x^4-1))/(x^3)

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

espandere dz(3xy^2-2x^2y+5)

e x p an d d z (3 x y^{2} - 2 x^{2} y + 5)

expand (4,7)vertice(4,-5)centro(4,2)

e x p an d (4, 7) v er t i ce (4, - 5) ce n t ro (4, 2)

espandere (-12x^2-16)/((2x+1)^2)

e x p an d \frac{- 12 x ^{2} - 16}{( 2 x + 1 ) ^{2}}

espandere (x+Δ)^2

e x p an d (x + Δ)^{2}