What is (sqrt(3)-i)^{11} ?

The solution to (sqrt(3)-i)^{11} is 1024sqrt(3)+1024i

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simplify (sqrt(3)-i)^{11}

simplify

(3 - i)^{11}

10243 + 1024 i

Solution steps

(3 - i)^{11}

Apply binomial theorem:

(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}

Expand summation

= \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}

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

\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}

Simplify

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

Rewrite in standard complex form:

10243 + 1024 i

= 10243 + 1024 i

\frac{( 2 x - 1 ) y}{( 2 x - 3 ) ( x - 1 )}

(5 x - y) (4 x + 3 y)

(x + 1) (1 - 3 x + 2)

4 (8 e + 7)

(1 + \frac{x}{2})^{9}

What is (sqrt(3)-i)^{11} ?
The solution to (sqrt(3)-i)^{11} is 1024sqrt(3)+1024i