What is ((sqrt(5)i)^4)/((4-3i)^2) ?

The solution to ((sqrt(5)i)^4)/((4-3i)^2) is 7/25+24/25 i

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simplify ((sqrt(5)i)^4)/((4-3i)^2)

simplify

\frac{( 5 i ) ^{4}}{( 4 - 3 i ) ^{2}}

\frac{7}{25} + \frac{24}{25} i

Solution steps

\frac{( 5 i ) ^{4}}{( 4 - 3 i ) ^{2}}

Simplify

(5 i)^{4} : 25

= \frac{25}{( 4 - 3 i ) ^{2}}

Expand

(4 - 3 i)^{2} : - 24 i + 7

= \frac{25}{- 24 i + 7}

Rewrite

- 24 i + 7

in standard complex form:

7 - 24 i

= \frac{25}{7 - 24 i}

Multiply by the conjugate

\frac{7 + 24 i}{7 + 24 i}

= \frac{25 ( 7 + 24 i )}{( 7 - 24 i ) ( 7 + 24 i )}

Simplify

\frac{25 ( 7 + 24 i )}{( 7 - 24 i ) ( 7 + 24 i )} : \frac{175 + 600 i}{625}

= \frac{175 + 600 i}{625}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{175}{625} + \frac{600}{625} i

Simplify

\frac{175}{625} + \frac{600}{625} i : \frac{7}{25} + \frac{24}{25} i

= \frac{7}{25} + \frac{24}{25} i

\frac{2 x + 3}{4} - \frac{x - 1}{2}

\frac{3 x ( 2 x 4 ^{3} )}{4}

ab \cdot (- a) b

\frac{- 4 + 3 - 25 + 17}{3 - - 9} - i

What is ((sqrt(5)i)^4)/((4-3i)^2) ?
The solution to ((sqrt(5)i)^4)/((4-3i)^2) is 7/25+24/25 i