I have no idea how much algabraic expansion you have done but to expand this equation you would:
(3+2i)^2 = (3+2i)(3+2i)
Expanding it gives 9 + 6i + 6i + 4(i^2) If you have never encountered this search "expanding double brackets"
Now we know that i = sqrt(-1) so naturally i^2 is just -1 so the equation becomes 9 + 6i + 6i +4(-1) -> 9 + 6i + 6i -4
Which, collecting like terms, makes 5 + 12i