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

w (x - 3, x + 3)

\frac{1}{( n + 2 ) ( n + 3 )}

- \frac{50 x}{( x ^{2} - 25 ) ^{2}}

3 x - 8 y - 2 z + 7 x + 3 y + z^{2}

\frac{( 2 - x ^{2} ) ^{2}}{2 e ^{5 x}}

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