Question 1143622
<pre>
{{{(x+yi)(4+3i)=7-4i}}}

FOIL out the left side:

{{{4x+3xi+4yi+3yi^2=7-4i}}}

Use the fact that i²= -1 to substitute (-1) for i²

{{{4x+3xi+4yi+3y(-1)=7-4i}}}

Simplify the third term on the left:

{{{4x+3xi+4yi-3y=7-4i}}}

The 2 REAL terms (that DON'T have i) on the left must 
equal the REAL term on the right (that DOESN'T have i) so:

{{{4x-3y=7}}}

The IMAGINARY terms on the left (that DO have i) must 
equal the IMAGINARY term on the right (that DOES have i), so:

{{{3xi+4yi=-4i}}}

Divide through by i:

{{{3x+4y=-4}}}

So we have the system of equations:

{{{system(4x-3y=7,3x+4y=-4)}}}

Solve that system (preferably by the elimination method):

{{{x=16/25}}} and {{{y=-37/25}}}

Edwin</pre>