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Verify the Caucy-riemann equations for the functions u(x,y), v(x,y) defined in the given domain u(x,y)=x³-3xy², v(x,y)=3x²y-y³,...

Verify the Caucy-riemann equations for the functions u(x,y), v(x,y) defined in the given domain

  1. u(x,y)=x³-3xy², v(x,y)=3x²y-y³, (x,y)ɛR
  2. u(x,y)=sinxcosy,v(x,y)=cosxsiny (x,y)ɛR
  3. u(x,y)=x/(x²+y²), v(x,y)=-y/(x²+y²),(x²+y²),   ( x²+y²)≠0
  4. u(x,y)=1/2 log(x²+y²), v(x,y)=sin¯¹(y/√¯x²+y²), ( x˃0 )                         

In each case,state a complex functions whose real and imaginary parts are u(x,y) and v(x,y)

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