Mastering Complex Variables
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Questions and Answers

Which one of the following is a necessary and sufficient condition for a complex variable function $f(z)$ to be analytic?

  • $f(z)$ has a harmonic conjugate
  • $f(z)$ is continuous
  • $f(z)$ has a limit at every point
  • $f(z)$ satisfies the Cauchy-Riemann equations in Cartesian coordinates (correct)

    • Which method can be used to determine an analytic function $f(z)$ when the real part $u$, imaginary part $v$, or their combination is given?

  • Cauchy-Riemann method
  • Milne-Thomson method (correct)
  • Orthogonal method
  • Harmonic method

    • What is the relationship between a harmonic function and its harmonic conjugate?

  • They are orthogonal trajectories
  • They have the same real part (correct)
  • They have the same imaginary part
  • They are analytic functions

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