What is (1-sqrt(3)i)^{11} ?

The solution to (1-sqrt(3)i)^{11} is 1024+1024sqrt(3)i

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simplify (1-sqrt(3)i)^{11}

simplify

(1 - 3 i)^{11}

1024 + 10243 i

Solution steps

(1 - 3 i)^{11}

Apply binomial theorem:

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

a = 1, b = - 3 i

= i = 0 \sum 11 (i 11) \cdot 1^{(11 - i)} (- 3 i)^{i}

Expand summation

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

Simplify

\frac{11 !}{0 ! ( 11 - 0 ) !} \cdot 1^{11} (- 3 i)^{0} : 1

Simplify

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

Simplify

\frac{11 !}{2 ! ( 11 - 2 ) !} \cdot 1^{9} (- 3 i)^{2} : 165 i^{2}

Simplify

\frac{11 !}{3 ! ( 11 - 3 ) !} \cdot 1^{8} (- 3 i)^{3} : - 4953 i^{3}

Simplify

\frac{11 !}{4 ! ( 11 - 4 ) !} \cdot 1^{7} (- 3 i)^{4} : 2970 i^{4}

Simplify

\frac{11 !}{5 ! ( 11 - 5 ) !} \cdot 1^{6} (- 3 i)^{5} : - 41583 i^{5}

Simplify

\frac{11 !}{6 ! ( 11 - 6 ) !} \cdot 1^{5} (- 3 i)^{6} : 12474 i^{6}

Simplify

\frac{11 !}{7 ! ( 11 - 7 ) !} \cdot 1^{4} (- 3 i)^{7} : - 89103 i^{7}

Simplify

\frac{11 !}{8 ! ( 11 - 8 ) !} \cdot 1^{3} (- 3 i)^{8} : 13365 i^{8}

Simplify

\frac{11 !}{9 ! ( 11 - 9 ) !} \cdot 1^{2} (- 3 i)^{9} : - 44553 i^{9}

Simplify

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

Simplify

\frac{11 !}{11 ! ( 11 - 11 ) !} \cdot 1^{0} (- 3 i)^{11} : - 2433 i^{11}

= 1 - 113 i + 165 i^{2} - 4953 i^{3} + 2970 i^{4} - 41583 i^{5} + 12474 i^{6} - 89103 i^{7} + 13365 i^{8} - 44553 i^{9} + 2673 i^{10} - 2433 i^{11}

Simplify

1 - 113 i + 165 i^{2} - 4953 i^{3} + 2970 i^{4} - 41583 i^{5} + 12474 i^{6} - 89103 i^{7} + 13365 i^{8} - 44553 i^{9} + 2673 i^{10} - 2433 i^{11} : 10243 i + 1024

= 10243 i + 1024

Rewrite in standard complex form:

1024 + 10243 i

= 1024 + 10243 i

6 (2 + 3)

(4 x + \frac{1}{4}) (4 x - \frac{1}{4})

2 (2 e^{x^{2}} x^{2} + e^{x^{2}})

(x - p + m) (x - p - m)

(5 (x + y) ln (x)) \frac{d x}{d y}

What is (1-sqrt(3)i)^{11} ?
The solution to (1-sqrt(3)i)^{11} is 1024+1024sqrt(3)i