Lets try something like your problems

(3+4i)(1+2i)

= 3*1 + 4i*1 + 3*2i + 4i*2i

= 3 + 4i + 6i + 8i^2

= 3 - 8 + 10i

= -5 + 10i.

See how it's done?

(3+4i) / ( 2+i )

= (3+4i)(2-i) / (2+i)(2-i) multiply by 1, where 1 = (2-i)/(2-i).

= multiply out the top / multiply out the bottom.