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Two harmonic functions \( u \) and \( v \) related by the Cauchy-Riemann equations are described as

  • A.orthogonal harmonic functions of the second kind
  • B.identical up to an additive constant
  • C.independent harmonic functions
  • D.conjugate harmonic functions

Answer: D

They are conjugate harmonic functions, and their level curves cross at right angles, since the Cauchy-Riemann equations make the two gradients perpendicular. Given one, the other is determined up to an additive constant, and the Milne-Thomson method recovers \( f(z) \) from either

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