pt

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

expandir (9+i)^5

Solução

expandir

(9 + i)^{5}

Solução

51804 + 31996 i

Passos da solução

(9 + i)^{5}

Aplicar o teorema do binômio:

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

a = 9, b = i

= i = 0 \sum 5 (i 5) \cdot 9^{(5 - i)} i^{i}

Expandir a soma

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 9^{5} i^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 9^{4} i^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 9^{3} i^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 9^{2} i^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 9^{1} i^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 9^{0} i^{5}

Simplificar

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 9^{5} i^{0} : 59049

Simplificar

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 9^{4} i^{1} : 32805 i

Simplificar

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 9^{3} i^{2} : 7290 i^{2}

Simplificar

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 9^{2} i^{3} : 810 i^{3}

Simplificar

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 9^{1} i^{4} : 45 i^{4}

Simplificar

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 9^{0} i^{5} : i^{5}

= 59049 + 32805 i + 7290 i^{2} + 810 i^{3} + 45 i^{4} + i^{5}

Simplificar

59049 + 32805 i + 7290 i^{2} + 810 i^{3} + 45 i^{4} + i^{5} : 31996 i + 51804

= 31996 i + 51804

Rewrite in standard complex form:

51804 + 31996 i

= 51804 + 31996 i

Exemplos populares

expandir (x-1)(x-1+sqrt(3))

e x p an d (x - 1) (x - 1 + 3)

expandir X(F(X)X+1=+1)

e x p an d X (F (X) X + 1 = + 1)

simplificar (-2-x)(-3/8-x)

s im pl i f y (- 2 - x) (- \frac{3}{8} - x)

expandir sqrt(2)(sqrt(8)-sqrt(3))

e x p an d 2 (8 - 3)

simplificar (x+2-sqrt(3))(x+2+sqrt(3))(x+6)

s im pl i f y (x + 2 - 3) (x + 2 + 3) (x + 6)