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

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Question 1143622: Given the equation (x+yi)(4+3i)=7-4i
Find x and y ?

Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


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

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Given the equation (x+yi)(4+3i)=7-4i
Find x and y ?
----------------
(x+yi)(4+3i)= 4x+3xi +4yi-3y
4x-3y + i*(3x+4y) = 7-4i
------
4x-3y = 7
3x+4y = -4
=================
Can you do the rest?

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