SOLUTION: Given the equation (x+yi)(4+3i)=7-4i Find x and y ?

FOIL out the left side:



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



Simplify the third term on the left:



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:



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



Divide through by i:



So we have the system of equations:



Solve that system (preferably by the elimination method):

 and 

Edwin