Mastering Complex Variables

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3 Questions

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

$f(z)$ satisfies the Cauchy-Riemann equations in Cartesian coordinates

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?

Milne-Thomson method

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

They have the same real part

This quiz covers topics related to complex variables, including functions of complex variables, limits, continuity, differentiability, and analytic functions. You will also learn about the necessary and sufficient conditions for a function to be analytic, the Cauchy-Riemann equations in Cartesian form, and the Milne-Thomson method for determining analytic functions. Additionally, the quiz explores harmonic functions, harmonic conjugates, and orthogonal trajectories. Test your understanding with this comprehensive complex variables quiz.

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