Complex analysis feels pristine and perfect, while real analysis seems messy and wild.
I think that the article has nailed it.swampwiz said:This author seems to say so:
https://blogs.scientificamerican.com/roots-of-unity/one-weird-trick-to-make-calculus-more-beautiful/
That downplays the amazing benefits of insisting on a well-defined complex derivative. It is a natural requirement to insist on and the consequences are profound and, IMHO, unexpected.Math_QED said:Of course you get a beautiful theory when you only study analytic functions! These functions are so well-behaved that everything works out smoothly (no pun intended).
Complex analysis is a branch of mathematics that deals with functions of complex numbers. It differs from real analysis in that it focuses on functions of complex variables, whereas real analysis deals with functions of real variables.
This is a subjective question and the answer may vary depending on the individual. However, many mathematicians and scientists find complex analysis to be easier because it has simpler and more elegant proofs compared to real analysis.
One of the main reasons complex analysis is considered easier is because the complex numbers form a more structured and complete number system compared to the real numbers. This allows for simpler and more powerful techniques to be used in complex analysis.
Having a strong foundation in real analysis can certainly be helpful in understanding complex analysis, but it is not a requirement. Many concepts in complex analysis can be understood without prior knowledge of real analysis.
Complex analysis has a wide range of applications in fields such as physics, engineering, and economics. It is used to model and analyze systems involving electrical circuits, fluid dynamics, and signal processing, among others.