Complex Numbers

 

Let $x$ and $y$ be complex numbers. If $x + y =2$    

and $xy = 5 - x^2 + xy - y^2$, then what is $x^2 + y^2$?    

 

ignoring  x + y  =  2    

 

considering                                 xy  =  5 – x² + xy – y²    

 

subtract xy from both sides          0  =  5 – x² – y²    

 

subtract 5 from both sides         – 5  =  – x² – y²    

 

multiply both sides by – 1              5  =  x² + y²    

 

                                                      x² + y²  =  5    

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