What is (-3sqrt(3)-3i)^5 ?

The solution to (-3sqrt(3)-3i)^5 is 3888sqrt(3)-3888i

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simplify (-3sqrt(3)-3i)^5

simplify

(- 33 - 3 i)^{5}

38883 - 3888 i

Solution steps

(- 33 - 3 i)^{5}

Apply binomial theorem:

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

a = - 33, b = - 3 i

= i = 0 \sum 5 (i 5) (- 33)^{(5 - i)} (- 3 i)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (- 33)^{5} (- 3 i)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (- 33)^{4} (- 3 i)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (- 33)^{3} (- 3 i)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (- 33)^{2} (- 3 i)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (- 33)^{1} (- 3 i)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (- 33)^{0} (- 3 i)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (- 33)^{5} (- 3 i)^{0} : - 21873

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (- 33)^{4} (- 3 i)^{1} : - 10935 i

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (- 33)^{3} (- 3 i)^{2} : - 72903 i^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (- 33)^{2} (- 3 i)^{3} : - 7290 i^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (- 33)^{1} (- 3 i)^{4} : - 12153 i^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (- 33)^{0} (- 3 i)^{5} : - 243 i^{5}

= - 21873 - 10935 i - 72903 i^{2} - 7290 i^{3} - 12153 i^{4} - 243 i^{5}

Simplify

- 21873 - 10935 i - 72903 i^{2} - 7290 i^{3} - 12153 i^{4} - 243 i^{5} : - 3888 i + 38883

= - 3888 i + 38883

Rewrite in standard complex form:

38883 - 3888 i

= 38883 - 3888 i

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

2 (x - 2 - x^{2})

(4 x^{2} + 9 \circ 3 x - 1) (x)

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

\frac{e ^{- π s}}{s ( s ^{2} + 1 )}

What is (-3sqrt(3)-3i)^5 ?
The solution to (-3sqrt(3)-3i)^5 is 3888sqrt(3)-3888i