• Given f(z)=$x^2+2axy+by^2+i(dx^2+2cky+y^2)$ is analytic,hence it satisfies Cauchy -Reimemann equations
• Comparing it with f(z)=u+iv we have u=$x^2+2axy+by^2$and v=$dx^2+2cky+y^2$
• Derivating u with respect to x we have

ux=2x+2ay

• Derivating u with respect to y we have

uy=2ax+2by

• Similarily for v we have

vx=2dx

vy=2ck+2y

• By C-R equations we have ux=vy and uy …