Q. A harmonic function is analytic if it satisfies the Laplace equation. If ๐ข(๐ฅ, ๐ฆ) = 2๐ฅ2 โ 2๐ฆ2 + 4๐ฅ๐ฆ is a harmonic function, then its conjugate harmonic function ๐ฃ(๐ฅ, ๐ฆ) is
(A) 4๐ฅ๐ฆ โ 2๐ฅ2 + 2๐ฆ2 + constant
(B) 4๐ฆ2 โ 4๐ฅ๐ฆ + constant
(C) 2๐ฅ2 โ 2๐ฆ2 + ๐ฅ๐ฆ + constant
(D) โ4๐ฅ๐ฆ + 2๐ฆ2 โ 2๐ฅ2 + constant
Ans: 4xy โ 2x2 + 2y2 + constant
Sol:
![Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]](https://www.gkseries.com/blog/wp-content/uploads/2023/10/Determine-the-correctness-or-otherwise-of-the-following-Assertion-A-and-the-Reason-R.jpg)
