What is ((1+sqrt(3)i)^8(sqrt(3)-i)^6)/((-1+i)^4) ?

The solution to ((1+sqrt(3)i)^8(sqrt(3)-i)^6)/((-1+i)^4) is -2048+2048sqrt(3)i

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simplify ((1+sqrt(3)i)^8(sqrt(3)-i)^6)/((-1+i)^4)

simplify

\frac{( 1 + 3 i ) ^{8} ( 3 - i ) ^{6}}{( - 1 + i ) ^{4}}

- 2048 + 20483 i

Solution steps

\frac{( 1 + 3 i ) ^{8} ( 3 - i ) ^{6}}{( - 1 + i ) ^{4}}

Simplify

(1 + 3 i)^{8} (3 - i)^{6} : - 81923 i + 8192

= \frac{- 8192 3 i + 8192}{( - 1 + i ) ^{4}}

Expand

(- 1 + i)^{4} : - 4

= \frac{- 8192 3 i + 8192}{- 4}

Factor out common term

8192 : 8192 (- 3 i + 1)

= \frac{8192 ( - 3 i + 1 )}{- 4}

Divide the numbers:

\frac{8192}{- 4} = - 2048

= - 2048 (- 3 i + 1)

Expand

- 2048 (- 3 i + 1) : 20483 i - 2048

= 20483 i - 2048

Rewrite in standard complex form:

- 2048 + 20483 i

= - 2048 + 20483 i

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

(0.8)^{2} - 0.25

cot (x) + tan (x)

cos (x) \cdot tan (x)

\frac{x ^{2} + 3 x - 18}{x ^{2} + 12 x + 36}

What is ((1+sqrt(3)i)^8(sqrt(3)-i)^6)/((-1+i)^4) ?
The solution to ((1+sqrt(3)i)^8(sqrt(3)-i)^6)/((-1+i)^4) is -2048+2048sqrt(3)i