Differential of a complex number

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Discussion Overview

The discussion revolves around the differentiation of a complex number with respect to the imaginary unit. Participants explore the implications of treating the imaginary unit as a variable versus a constant within the context of complex analysis.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant asks for the derivative of a complex number expressed as \(x + iy\) with respect to \(i\).
  • Another participant suggests that the derivative is \(y\), assuming standard conventions in real and complex analysis apply.
  • Some participants question whether the imaginary unit \(i\) should be considered a constant in this context.
  • There is acknowledgment that the original poster treats \(i\) as a variable, which adds complexity to the discussion.

Areas of Agreement / Disagreement

Participants express differing views on whether the imaginary unit is a constant or a variable, indicating that the discussion remains unresolved.

Contextual Notes

The discussion may depend on specific definitions of differentiation in complex analysis, and the treatment of \(i\) as a variable or constant is not universally agreed upon.

VaccumEnergy
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What is d/di(x+iy)?
 
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VaccumEnergy said:
What is d/di(x+iy)?

I'm guessing you meant

$$\frac{d}{di}(x+iy)=y$$

Assuming all the usual stuff in real and complex analysis apply here, of course.

DonAntonio
 
Isn't the imaginary unit a constant?
 
Klungo said:
Isn't the imaginary unit a constant?


I guess it is, yet the OP regards it as a variable in his question, so...

DonAntonio
 

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