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:
