Is complex analysis really much easier than real analysis?

[swampwiz]

This author seems to say so:

https://blogs.scientificamerican.com/roots-of-unity/one-weird-trick-to-make-calculus-more-beautiful/

Complex analysis feels pristine and perfect, while real analysis seems messy and wild.

 

[BvU]

Have you read @LCKurtz

There's nothing imaginary about complex numbers​

 

[FactChecker]

This author seems to say so:

https://blogs.scientificamerican.com/roots-of-unity/one-weird-trick-to-make-calculus-more-beautiful/

I think that the article has nailed it.

 

[member 587159]

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).

 

[FactChecker]

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).

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.