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Find an analytic function f(z)=u+iv where. \[ u-v = \dfrac {x-y}{x^2 + 4xy - y^2} \]
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written 4.5 years ago by
teamques10
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$f(z) = u + iv .................(i)\ Multiplying\ equation\ (i)\ by\ i\ \therefore\ if(z)=iu-v .................(ii)\ Adding\ equation\ (i)\ and\ (ii)\ \ \therefore\ f(z)+if(z)=u+iv+iu-v\ \therefore\ (1+i)f(z)=(u-v)+i(u+v)\ Let\ u-v = P\ and\ u+v=Q\ \therefore\ (1+i)f(z)=P+iQ ...............(iii)\ Since, \ f(z)\ is\ analytic,\ (1+i)\ f(x)\ is\ also\ analytic\ where\ (1+i)\ is\ constant.\ As\ the\ function\ …
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