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

1. anonymous

this is a repeat yes?

2. anonymous
3. Mertsj

I don't know;.

4. Mertsj

smarty pants

5. anonymous

maybe it was not clear, but you have to square the denominator to see what it actually is, then multiply top and bottom by the conjugate of the denominator to see what you get.

6. Mertsj

What difference does it make?

7. Mertsj

|dw:1328415021324:dw|

8. anonymous

$\frac{5i}{(2+3i)^2}$ $=\frac{5i}{4+12i+9i^2}$ $=\frac{5i}{4-9+12i}=\frac{5i}{12i-5}$ $=(\frac{5i}{12i-5})(\frac{12i+5}{12i+5})$ $=\frac{60i^2+25i}{144i^2-25}=\frac{-60+25i}{-144-25}=\frac{-60+25i}{-169}=\frac{60-25i}{169}$