What is ((-sqrt(3)+i)^6)/((1-i)^{10)} ?

The solution to ((-sqrt(3)+i)^6)/((1-i)^{10)} is -2i

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simplify ((-sqrt(3)+i)^6)/((1-i)^{10)}

simplify

\frac{( - 3 + i ) ^{6}}{( 1 - i ) ^{10}}

- 2 i

Solution steps

\frac{( - 3 + i ) ^{6}}{( 1 - i ) ^{10}}

Expand

(- 3 + i)^{6} : - 64

= \frac{- 64}{( 1 - i ) ^{10}}

Expand

(1 - i)^{10} : - 32 i

= \frac{- 64}{- 32 i}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{64}{32 i}

Factor the number:

64 = 32 \cdot 2

= \frac{32 \cdot 2}{32 i}

Cancel the common factor:

32

= \frac{2}{i}

Simplify

\frac{2}{i} : - 2 i

= - 2 i

\frac{( 6 ^{3} \cdot 6 ^{2} ) ^{2}}{( 6 ^{4} ) ^{- 2}}

1 0^{2} - 5^{2}

(1 + 2 i) (3 - i)

\frac{4 r ^{2}}{r}

What is ((-sqrt(3)+i)^6)/((1-i)^{10)} ?
The solution to ((-sqrt(3)+i)^6)/((1-i)^{10)} is -2i