Question 124825
You need to remember the 'difference of two squares' factorization: {{{(a+b)(a-b)=a^2-b^2}}}


What we want to accomplish is to get that pesky i out of our denominator.  Using the difference of two squares idea, we see that we can accomplish this quite nicely by multiplying the denominator by {{{2-3i}}}.  Of course if we multiply the denominator by something, we must multiply the numerator by the same thing, so:


{{{((4-5i)/(2+3i))((2-3i)/(2-3i))}}}


Using the difference of two squares on the denominator, and FOIL on the numerator we obtain:


{{{(8-12i-10i+15i^2)/(4-9i^2)}}}.


Now, collect terms remembering that {{{i^2=-1}}}.


{{{((-7)-22i)/13}}}


In {{{a+bi}}} form you have:  {{{-(7/13)-(22/13)i}}}