What is (sqrt(3)-sqrt(3)i)^7 ?

The solution to (sqrt(3)-sqrt(3)i)^7 is 216sqrt(3)+216sqrt(3)i

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simplify (sqrt(3)-sqrt(3)i)^7

simplify

(3 - 3 i)^{7}

2163 + 2163 i

Solution steps

(3 - 3 i)^{7}

Apply binomial theorem:

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

a = 3, b = - 3 i

= i = 0 \sum 7 (i 7) (3)^{(7 - i)} (- 3 i)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} (3)^{7} (- 3 i)^{0} : 273

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} (3)^{6} (- 3 i)^{1} : - 1893 i

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} (3)^{5} (- 3 i)^{2} : 5673 i^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} (3)^{4} (- 3 i)^{3} : - 9453 i^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} (3)^{3} (- 3 i)^{4} : 9453 i^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} (3)^{2} (- 3 i)^{5} : - 5673 i^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} (3)^{1} (- 3 i)^{6} : 1893 i^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} (3)^{0} (- 3 i)^{7} : - 273 i^{7}

= 273 - 1893 i + 5673 i^{2} - 9453 i^{3} + 9453 i^{4} - 5673 i^{5} + 1893 i^{6} - 273 i^{7}

Simplify

273 - 1893 i + 5673 i^{2} - 9453 i^{3} + 9453 i^{4} - 5673 i^{5} + 1893 i^{6} - 273 i^{7} : 2163 + 2163 i

= 2163 + 2163 i

\frac{1}{( x ^{2} + 4 ) ( x + 2 )}

3 (\frac{3 π}{2} - \frac{9 3}{4})

(7 - \frac{x ^{2}}{2})^{2}

\frac{6}{( s ^{2} + 9 ) ^{2}}

(\frac{1}{2 x} + 4) (\frac{1}{2 x} - 8)

What is (sqrt(3)-sqrt(3)i)^7 ?
The solution to (sqrt(3)-sqrt(3)i)^7 is 216sqrt(3)+216sqrt(3)i