This is now post number 278 on this website and to be honest the content of this post should have been here years ago. This post is about complex integration and I more or less compare how you do that in the complex plane against how it is done in 3D space.
Integrating the identity simple means integrating zdz on the complex plane and XdX on the space of 3D complex numbers. Of course I have used complex integration in higher dimensional spaces in the past when I needed it. For example this is how I found my first number tau: On the space of 3D complex numbers you must find the logarithm of j^2 (not j because j has a determinant of minus one) and I did that with complex integration.
For people who are new to this website: j denotes the imaginary unit in 3D space and it’s third power equals -1. That mimics the situation in the complex plane where the imaginary unit i if you square it that gives -1.

All these years I never used complex integration just to find a primitive, so that is done in this post. And since we are integrating zdz we expect to find 0.5z^2on the complex plane while on my beloved space of 3D complex numbers the integral of XdX should yield 0.5X^2.
Of course we will find these results because otherwise I would have been very stupid in say the last 15 years. Of course just like every body elso I have been very stupid on many occasions on such long timescales, but not when it comes to 3D complex numbers.

Oops, I see I still have to make the seven png pictures but that won’t take very much time. So that’s this math post: 7 pictures of each 550×1500 pixels in size. I hope that after reading it you can also perform complex integration is say the space of 4D complex numbers.
And now we talk about 4D numbers; I also included at the end the famous quaternions and of course if we try to integrate them we get the usual garbage once more demonstrating that when it comes to differentiation and integration the quaternions are just awful.

That was it for this math post. Likely the next post is another video where the famous Stern Gerlach experiment is explained. Of course in such videos they never jump to the correct conclusion that says it is very likely that electron magnetism is monopole in nature. Just like their electric charge by the way, of course for all professional physics persons the electron has to be a tiny magnet. Not that they have much so called ‘five sigma’ experimental evidence for that, but for them this is not a problem…

Ok, let me hit that button ‘publish website’ and may I thank you for your attention.