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If u = x2 – y2, then the conjugate harmonic function is
  • a)
    2xy
  • b)
    x2 + y2
  • c)
    y2 – x2
  • d)
    -x2 – y2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If u = x2 – y2, then the conjugate harmonic function isa)2xyb)x2...
Concept:
If two functions u and v satisfy Cauchy-Riemann equations, then they are said to be harmonic conjugates with respect to each other.
Cauchy-Riemann equations are 
vy = ux
vx = - uy
Calculation:
Given u = x2 – y2, let v be the harmonic conjugate.
By Cauchy-Riemann equations,
vy = ux = 2x; vx = - uy = - (-2y) = 2y;
We have dv = vx dx + vy dy 
⇒ dv = 2y dx + 2x dy = d(2xy)
⇒ v = 2xy + k or v = 2xy
∴ The conjugate harmonic function is 2xy
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Community Answer
If u = x2 – y2, then the conjugate harmonic function isa)2xyb)x2...
If u = x^2, it means that the variable "u" is equal to the square of the variable "x".
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