Question: Given the function (u(x, y)=x^{2}-y^{2}). (a) Prove that this equation satisfies the Laplace equation. (b) Find the function (v(x, y)) such that (f(z)=u+i v) is

Given the function $u(x, y)=x^{2}-y^{2}$.

(a) Prove that this equation satisfies the Laplace equation.

(b) Find the function $v(x, y)$ such that $f(z)=u+i v$ is an analytic function.

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