Analogous

 For those feeling uneasy about not really understanding about how

e^i*theta represents movement around the unit circle. I have found a reference

to that very issue in a help site  for French junior college. e^i*pi/2... is a complex

number of module 1 and an angle argument. This choice of notation  arises as an

an analogy to exponentiation and is something to be justified.

Eventually, we need to work with sine and cosine functions to appreciate what is 

going on.

https://www.educastream.com/fr/complexes-forme-exponentielle-terminale-s#:~:text=ei%CE%B8%20est%20le%20nombre,i%CE%B8%20%2C%20%CE%B8%20%C3%A9tant%20son%20argument.

The choice of e - exponential - is clear because one can work with it easily.

With a calculator, one uses the ln function!

Call pi, divided by 2:

                                                              

Call the ln of this value:

Add to memory:

Clear, and call e:

Raise to the value of memory:

Multiply by 2:

Working with logarithms has advantages. The log numbers change on a multiplication

scale. This is true for both ln(x) on e, log(x). Below:

Still, working with e is much preferred. From Merlin!

The derivatives:

                                                                  

The integrals:

                                                                             

The change of base formulas from Copilot:

                                                                      

                                                                                  *     *     *

Today, I go for my annual flu shot. I expect to be feverish and cold, and out of commission

till tomorrow. 🧛‍♂️