en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (sqrt(3)+i)^9

Solution

simplify

(3 + i)^{9}

Solution

- 512 i

Solution steps

(3 + i)^{9}

Apply binomial theorem:

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

a = 3, b = i

= i = 0 \sum 9 (i 9) (3)^{(9 - i)} i^{i}

Expand summation

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

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} (3)^{9} i^{0} : 813

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} (3)^{8} i^{1} : 729 i

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} (3)^{7} i^{2} : 9723 i^{2}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} (3)^{6} i^{3} : 2268 i^{3}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} (3)^{5} i^{4} : 11343 i^{4}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} (3)^{4} i^{5} : 1134 i^{5}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} (3)^{3} i^{6} : 2523 i^{6}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} (3)^{2} i^{7} : 108 i^{7}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} (3)^{1} i^{8} : 93 i^{8}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} (3)^{0} i^{9} : i^{9}

= 813 + 729 i + 9723 i^{2} + 2268 i^{3} + 11343 i^{4} + 1134 i^{5} + 2523 i^{6} + 108 i^{7} + 93 i^{8} + i^{9}

Simplify

813 + 729 i + 9723 i^{2} + 2268 i^{3} + 11343 i^{4} + 1134 i^{5} + 2523 i^{6} + 108 i^{7} + 93 i^{8} + i^{9} : - 512 i

= - 512 i

Popular Examples

simplify (63)/((-7))simplify

\frac{63}{( - 7 )}

simplify sqrt(3)*sqrt(13)simplify

3 \cdot 13

simplify sqrt(7300)simplify

7300

simplify ((x^3-125))/((x-5))simplify

\frac{( x ^{3} - 125 )}{( x - 5 )}

simplify 11x-7+3x+9 simplify

11 x - 7 + 3 x + 9

Frequently Asked Questions (FAQ)

What is (sqrt(3)+i)^9 ?
The solution to (sqrt(3)+i)^9 is -512i