What is (5i)/((2+3i)^2) ?

The solution to (5i)/((2+3i)^2) is 60/169-i 25/169

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simplify (5i)/((2+3i)^2)

simplify

\frac{5 i}{( 2 + 3 i ) ^{2}}

\frac{60}{169} - i \frac{25}{169}

Solution steps

\frac{5 i}{( 2 + 3 i ) ^{2}}

(2 + 3 i)^{2} = - 5 + 12 i

= \frac{5 i}{( - 5 + 12 i )}

Remove parentheses:

(- a) = - a

= \frac{5 i}{- 5 + 12 i}

Rationalize

\frac{5 i}{- 5 + 12 i} : \frac{60 - 25 i}{169}

= \frac{60 - 25 i}{169}

Rewrite

\frac{60 - 25 i}{169}

in standard complex form:

\frac{60}{169} - \frac{25}{169} i

= \frac{60}{169} - \frac{25}{169} i

s^{2} - 4 s t - 12 t^{2}

(- 6 + i) (- 6 - i)

- 5 x^{2} + 13 x - 6

\frac{10 + 8 i}{- 4 i}

\frac{x ^{2} + y ^{2}}{x ^{2} - y ^{2}}