prove that x^2+y^2+ln(x^2+y^2)/2 is harmonic function and find it’s harmonic conjugate

Introduction : A harmonic function is a function that satisfies Laplace equation. Harmonic functions are useful for analysis of analytic function and determining it’s harmonic conjugate.Question: Prove that \( u=x^2-y^2+\frac{1}{2}\ln{\left(x^2+y^2\right)}\) is harmonic and find it’s harmonic conjugate.\[\]Solution: A function \(u\left(x,…

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