## anonymous 4 years ago 5i/(2+3i)^2 Write the quotient in standard form

1. anonymous

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

2. anonymous

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 $\frac{-5-12i}{-5-12I}$

3. anonymous

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 $\frac{60}{169}-\frac{25}{19}i$

4. anonymous

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