Questions tagged [complex-analysis]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3
votes
2answers
360 views

Introduction of $\imath$ and $\jmath$ notations for the imaginary unit

The imaginary unit is generally denoted $i$ or $\imath$. I have learned that the term imaginary ("imaginaires") was coined by R. Descartes in 1637, and the "i" notation was introduced by L. Euler (cf. ...
36
votes
1answer
2k views

What was Euler's motivation for introducing $i$ for $\sqrt{-1}$?

[Mauro Allegranza has answered the question of who introduced the notation $i$ (Euler, followed later by Gauss), so I have changed the title. I have also edited the question in other ways to make it ...
11
votes
3answers
4k views

Why are quaternions more popular than tessarines despite being non-commutative?

Is this simply because of marketing, hype, etc? The bicomplex numbers (especially tessarines) look just great being commutative and all. Images source:https://citeseerx.ist.psu.edu/viewdoc/download?...
6
votes
1answer
402 views

Who came up with the link between the spectrum of an operator and the poles of a meromorphic function?

From Dieudonné's "History of Functional Analysis" I learned that Picard in 1893 gave a characterization of an eigenvalue of the Laplacian as the simple pole of a meromorphic function. Is there an ...
9
votes
1answer
819 views

Who was the first person to notice logarithms of negatives numbers and for what reason?

Who was the first person to notice logarithms of negatives numbers and why? When did they first arise naturally? I thought I saw somewhere that it had to do with integration but I can't find it ...
8
votes
2answers
326 views

First papers on holomorphic functions

Briot and/or Cauchy are often said to have written the first papers on holomorphic functions, explicitly discussing them as such and their special properties. Which papers are these? When and where ...
8
votes
1answer
9k views

Euler's first proof of $e^{ix}=\cos(x)+i\sin(x)$

What was Eulers first proof of his famous formula? In Euler's book on complex functions he used the following proof. But was this his first proof? Euler starts with writing down De Moivre's Formula (...
3
votes
1answer
164 views

Were complex number first considered of limited usefulness?

Were complex numbers ever considered to be of limited usefulness that is not very useful in practice (unlike modern science where we strongly need complex numbers)? Note my question is not about ...
5
votes
1answer
635 views

What was the motivation for Cauchy's Integral Theorem?

How did Cauchy go about Cauchy's integral theorem? What was his motivation?