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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

Mastering Complex Variables

Choose a study mode

Podcast

Questions and Answers

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

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?

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

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