What is ((2+2i)^8)/((-5+5i)^2) ?

The solution to ((2+2i)^8)/((-5+5i)^2) is (2048i)/(25)

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simplify ((2+2i)^8)/((-5+5i)^2)

simplify

\frac{( 2 + 2 i ) ^{8}}{( - 5 + 5 i ) ^{2}}

\frac{2048 i}{25}

Solution steps

\frac{( 2 + 2 i ) ^{8}}{( - 5 + 5 i ) ^{2}}

(- 5 + 5 i)^{2} = - 50 i

= \frac{( 2 + 2 i ) ^{8}}{- 50 i}

(2 + 2 i)^{8} = 4096

= \frac{4096}{- 50 i}

Apply the fraction rule:

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

= - \frac{4096}{50 i}

Cancel the common factor:

2

= - \frac{2048}{25 i}

Rationalize

- \frac{2048}{25 i} : \frac{2048 i}{25}

= \frac{2048 i}{25}

(- \frac{4}{5})^{5}

(4 b^{2} - 8 b + 11) - (- 2 b^{2} - 4 b + 5)

(x^{- 1})^{- 2}

(x^{2} - 2 x - 8) (- x^{2} + 3 x - 5)

\frac{x ^{2} + 4 x - 21}{x ^{2} - 9}

What is ((2+2i)^8)/((-5+5i)^2) ?
The solution to ((2+2i)^8)/((-5+5i)^2) is (2048i)/(25)