What is expand ((1-2i)^{10})/((2+2i)^5) ?

The solution to expand ((1-2i)^{10})/((2+2i)^5) is -3353/256-(2879i)/(256)

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expand ((1-2i)^{10})/((2+2i)^5)

expand

\frac{( 1 - 2 i ) ^{10}}{( 2 + 2 i ) ^{5}}

- \frac{3353}{256} - \frac{2879 i}{256}

Solution steps

\frac{( 1 - 2 i ) ^{10}}{( 2 + 2 i ) ^{5}}

(2 + 2 i)^{5} = - 128 - 128 i

= \frac{( 1 - 2 i ) ^{10}}{( - 128 - 128 i )}

(1 - 2 i)^{10} = 237 + 3116 i

= \frac{237 + 3116 i}{( - 128 - 128 i )}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 237, b = 3116, c = - 128, d = - 128

= \frac{( 237 ( - 128 ) + 3116 ( - 128 ) ) + ( 3116 ( - 128 ) - 237 ( - 128 ) ) i}{( - 128 ) ^{2} + ( - 128 ) ^{2}}

Refine

= \frac{- 429184 - 368512 i}{32768}

Simplify

\frac{- 429184 - 368512 i}{32768} : - \frac{3353 + 2879 i}{256}

= - \frac{3353 + 2879 i}{256}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{3353 + 2879 i}{256} = - (\frac{3353}{256}) - (\frac{2879 i}{256})

= - (\frac{3353}{256}) - (\frac{2879 i}{256})

Remove parentheses:

(a) = a

= - \frac{3353}{256} - \frac{2879 i}{256}

\frac{d}{d t} ((t) (k (t - C)))

\frac{1}{( 1 - x ) ( b - x ) ( d - x )}

2 (x + Δ x) - 1

α (5, - 1, 2) + β (- 7, - 2, 11)

(5 y + 12 x yz - 10 + 6 x^{4}) - (12 +, + 4 x)

What is expand ((1-2i)^{10})/((2+2i)^5) ?
The solution to expand ((1-2i)^{10})/((2+2i)^5) is -3353/256-(2879i)/(256)