A harmonic function is analytic if it satisfies the Laplace equation. If 𝑢(𝑥, 𝑦) = 2𝑥2 − 2𝑦2 + 4𝑥𝑦 is a harmonic

Q. A harmonic function is analytic if it satisfies the Laplace equation. If 𝑢(𝑥, 𝑦) = 2𝑥² − 2𝑦² + 4𝑥𝑦 is a harmonic function, then its conjugate harmonic function 𝑣(𝑥, 𝑦) is

             (A) 4𝑥𝑦 − 2𝑥² + 2𝑦² + constant

             (B) 4𝑦² − 4𝑥𝑦 + constant

             (C) 2𝑥² − 2𝑦² + 𝑥𝑦 + constant

             (D) −4𝑥𝑦 + 2𝑦² − 2𝑥² + constant

Ans: 4xy − 2x² + 2y² + constant

Sol: