[tex](4+2i)(-3-5i)\qquad\text{use distributive property}\\\\=(4)(-3)+(4)(-5i)+(2i)(-3)+(2i)(-5i)\\\\=-12-20i-6i-10i^2\qquad\text{used}\ i^2=-1\\\\=-12-26i-10(-1)\\\\=-12-26i+10\\\\=\boxed{-2-26i}[/tex]
[tex](3-4i)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=3^2-2(3)(4i)+(4i)^2\\\\=9-24i+16i^2\qquad\text{use}\ i^2=-1\\\\=9-24i+16(-1)\\\\=9-24i-16\\\\=\boxed{-7-24i}[/tex]
