Question 283669
(4+5i)(2-3i)



Use FOIL (first outside inside last)



First:  {{{4 * 2 = 8}}}
Outside: {{{4 * (-3i) = -12i}}}
Inside:  {{{(5i) * 2 = 10i}}}
Last:  {{{5i * (-3i) = -15i^2}}}


Let's put it all together:   {{{8 - 12i + 10i -15i^2}}}
Combine like terms:  {{{8 -2i - 15i^2}}}



We're not done yet.  See the {{{-15i^2}}}? 
Well, {{{i^2}}} = {{{-1}}}


Therefore, for {{{-15i^2}}} you really have:  {{{(-15)(-1)}}} which is:  15


THEREFORE... you really have 8 - 2i + 15, which is.....
23 - 2i



See how that worked out?  I hope this helps you.  :-)