harmonic conjugate

$$f\left( z \right) = u\left( {x,y} \right) + i\,\,\,\,v\left( {x,y} \right)$$ is an analytic function of complex variable $$z=x+iy$$ , where $$i = \sqrt { - 1} $$ If $$u(x,y)=2xy,...

An analytic function of a complex variable $$z = x + iy$$ is expressed as $$f\left( z \right) = u\left( {x + y} \right) + iv\left( {x,y} \right),$$ where $$i = \sqrt { - 1} .$$ If...