http://google.com, pub-7771400403364887, DIRECT, f08c47fec0942fa0 If x=2 with f(z)=1/z then solve

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If x=2 with f(z)=1/z then solve

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If f(z)= 2 with f(z)=1/z find the solution of the equation 
f(z)=1/z=(x-iy)/x²+y²=x/(x²+y²) -iy/x²+y²

HINT. 

z=(x+iy) and here we are aware that 1/z is same as 1/x+iy  hence rationalize the denominator .

Therefore 

x= u/(u²+v²) and y= v/(u²+v²)  

Therefore  

u/(u²+v²)=2

u= 2u²+v²

2u²-u+2v²=0

U²-u/2+v²=0

Completing square method 

U²-u/2+(-1/4)²+v²=(-1/4)²

U²-u/2+(-1/4)²+v²=1/16


Factorizing 

(U-1/4)²+v²=1/16

Which is a circle center (1/4,0) and radius r=1/4

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