Question

5i/(2+3i)^2
Write the quotient in standard form

Answer 1

you will need so square the denomniator first and see what you get

Answer 2

you should get
\[(2+3i)^2=-5+12i\] so your next step is to divide
\[\frac{5i}{-5+12i}\]and you do this by multiplying numerator and denominator by the conjugate of the denominator, in other words multiply by
\[\frac{-5-12i}{-5-12I}\]

Answer 3

the denominator will be
\[5^2+12^2=169\] and the numerator will be
\[5i(-5-12i)\] or
\[-25i+60\] giving your final answer as
\[\frac{60}{169}-\frac{25}{19}i\]

Answer 4

typo on last line
\[\frac{60}{169}-\frac{25}{169}i\]