Cauchy-Riemann Equations test problem

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Discussion Overview

The discussion revolves around a problem related to the Cauchy-Riemann equations, focusing on identifying the correct choice for a mathematical assignment involving partial derivatives of a complex function. Participants are exploring the real and imaginary parts of the function and their derivatives.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about which answer choice is correct and seeks help.
  • Another participant asks for the real part of the function and its partial derivative with respect to x, indicating a focus on the mathematical details.
  • Some participants suggest that the answer might be choice D based on their calculations involving partial derivatives.
  • A participant expresses reluctance to validate answers for what they perceive as an online exam, but later clarifies that it is an assignment.
  • One participant provides the expressions for the real part (u) and imaginary part (v) of the function, suggesting that the necessary partial derivatives can be evaluated from these.
  • A later reply thanks the participant for providing guidance on the problem.

Areas of Agreement / Disagreement

There is no clear consensus on the correct answer choice, as participants express differing views on the nature of the inquiry and the validity of the answers being sought.

Contextual Notes

Participants have not fully established the definitions of u and v before proceeding with their evaluations, which may affect the clarity of the discussion.

jaychay
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I cannot figure it out which choice is correct
Please help me
Please!
Thank you in advance
 
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What is the real part of $f(x+iy)$? That is $u(x,y)$.
What is its partial derivative with respect to $x$? That is $u_x$.
 
Klaas van Aarsen said:
What is the real part of $f(x+iy)$? That is $u(x,y)$.
What is its partial derivative with respect to $x$? That is $u_x$.
Is the correct answer is choice D ?
I already done it by using partial derivatives and compare them
 
jaychay said:
Is the correct answer is choice D ?
I already done it by using partial derivatives and compare them
It seems you are doing some online exam.
I'd rather not validate answers for something like that.
 
Klaas van Aarsen said:
It seems you are doing some online exam.
I'd rather not validate answers for something like that.
Sir, it's not an online exam
It's my assignment that I try to do on my own
I translate it from my math textbook in my country into English
I really want to become better at math.

If you still don't believe or you think I try to lie to you
Here is the original form of math textbook in my country

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Have you at least established what your u and v are?

As Klaas stated, $\displaystyle \begin{align*} u = \mathcal{Re}\left( f \right) = \mathrm{e}^x \left[ y + \cos{ \left( y \right) } \right] \end{align*}$ and $\displaystyle \begin{align*} v = \mathcal{Im}\left( f \right) = \mathrm{e}^x \sin{ \left( y \right) } \end{align*}$. Surely you can evaluate the necessary partial derivatives and make a judgement...
 
Prove It said:
Have you at least established what your u and v are?

As Klaas stated, $\displaystyle \begin{align*} u = \mathcal{Re}\left( f \right) = \mathrm{e}^x \left[ y + \cos{ \left( y \right) } \right] \end{align*}$ and $\displaystyle \begin{align*} v = \mathcal{Im}\left( f \right) = \mathrm{e}^x \sin{ \left( y \right) } \end{align*}$. Surely you can evaluate the necessary partial derivatives and make a judgement...
Thank you very much for guiding it for me.
 

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