What is expand ((2+4i)^4)/((6+5i)^4) ?

The solution to expand ((2+4i)^4)/((6+5i)^4) is -117232/13845841+(1483776i)/(13845841)

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expand ((2+4i)^4)/((6+5i)^4)

expand

\frac{( 2 + 4 i ) ^{4}}{( 6 + 5 i ) ^{4}}

- \frac{117232}{13845841} + \frac{1483776 i}{13845841}

Solution steps

\frac{( 2 + 4 i ) ^{4}}{( 6 + 5 i ) ^{4}}

(6 + 5 i)^{4} = - 3479 + 1320 i

= \frac{( 2 + 4 i ) ^{4}}{( - 3479 + 1320 i )}

(2 + 4 i)^{4} = - 112 - 384 i

= \frac{( - 112 - 384 i )}{( - 3479 + 1320 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 = - 112, b = - 384, c = - 3479, d = 1320

= \frac{( - 112 ( - 3479 ) + ( - 384 ) \cdot 1320 ) + ( - 384 ( - 3479 ) - ( - 112 ) \cdot 1320 ) i}{( - 3479 ) ^{2} + 132 0 ^{2}}

Refine

= \frac{- 117232 + 1483776 i}{13845841}

Apply the fraction rule:

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

\frac{- 117232 + 1483776 i}{13845841} = - \frac{117232}{13845841} + \frac{1483776 i}{13845841}

= - \frac{117232}{13845841} + \frac{1483776 i}{13845841}

\frac{( 2 s - 105 ) ( 4 s - 10945 )}{8}

\frac{d x}{( a - x ) ^{3}}

p (x, y) A (- 3, - 4) B (1, 2)

\frac{d}{d x} ((z) (\frac{y}{x + y} - z))

\frac{r ( 9 - 2 r )}{( r ^{2} - 9 r - 9 )}

What is expand ((2+4i)^4)/((6+5i)^4) ?
The solution to expand ((2+4i)^4)/((6+5i)^4) is -117232/13845841+(1483776i)/(13845841)