SOLUTION: {{{((1+i)/(1-i))^2 + 1/(x+iy) = 1+i}}}

 

We simplify what's squared in the the first term



Now we square it to get the complete first term simplified:



Substituting -1 for the first term



Add 1 to both sides:



Multiply both sides by (x + iy)



FOIL out the right side:







Set the real terms on the left equal to the real terms on the right:



Set the imaginary terms on the left equal to the imaginary terms on
the right (there aren't any on the left so we use 0):



divide through by i



Solve the system:



Solve the first equation for y



Substitute in the 2nd equation of the system:



Distribute:



Combine terma:



Add 2 to both sides:



Divide both sides by 5



Substitute for x in







Multiple through by 5





Divide both sides by 5

 



Edwin