# Math Help - simplify equation

1. ## simplify equation

Hi guys
i am trying to solve some math questions for fun and i faced a problem
the question says simplify the following equation :
3-2i/3+2i

2. Multiply both the top and bottom with the denominator's conjugate:

$\frac{3-2i}{3+2i} \times \frac{3-2i}{3-2i}$

3. I tried but no real simplification happens

4. It's simplified because you end up with one complex number, instead of a complex number divided by another. This makes it easier to use this expression to solve complex number problems.

5. can you please show me how to do it please because i couldont do it

6. $\frac{3-2i}{3+2i} \times \frac{3-2i}{3-2i}$

$= \frac{9 - 6i - 6i + 4i^2}{9 -6i + 6i - 4i^2}$

$= \frac{9 + 4(-1) - 12i}{9-4(-1)}$

$= \frac{5 - 12i}{13}= \frac{5}{13} - \frac{12i}{13}$

7. Thank you very much ,, i forgot that i^2=-1