Re: Practical applications of complex numbers

On 01/08/2026 9:20 PM, Stefan Ram wrote:
> Johann 'Myrkraverk' Oskarsson <[email protected]> wrote or quoted:
>> Can you please fill me in on more useful practical applications of
>> complex numbers than just the Mandelbrot visualization?
> 
>    Physics is full of them, especially in quantum theory.
> 
>    The following example does not actually require quantum theory:
> 
>    A /glass plate/ can shift the phase of a light beam travelling
>    through it. A plate with a certain thickness d will change the
>    amplitude from a to -a.
> 
>    Change of amplitude from a to -a
> 
>    Before
> 
> |          .....---...
> |      ...''         ''..                                             ..
> |    ..'                ''..                                        ..'
> | ..''                     `'.                                   ..'
> |.'                          `'.                               ..'
> |-------------------------------`----------------------------.''--------
> |                                `'..                      ..'
> |                                   `..                 ..'
> |                                     ''..           ...'
> |                                         ''-.......''
> 
>    After
> 
> |
> |                                         .....'--...
> |                                      ..''         '''..
> |                                   ..''                ''.
> |                                 ..'                     `'.
> |                               ..'                          '..
> |-.---------------------------:'-------------------------------`--------
> | `'.                      ..'                                   `'.
> |   `'..                 ..'                                       `'..
> |      ''..          ...''                                            ''
> |         ''--......''
> |

This is some beautiful ASCII art rendering of waves.  Do you have a tool
that does this, or do you keep this pre-rendered in a text file for just
such occasions?
I'm not asking completely idly, I am wondering if I can make such a tool
myself.  Preferably without resorting to look at anything but the output
above; I mean, not any ready made source code.

Cross posting to alt.ascii-art, and you can see some of my old art re-
posted there recently.

> 
>    Introducing /two/ such plates, we get -(-a), which is the original
>    wave again.
> 
>    Each plate multiplies the amplitude by -1, and their combination has
>    the effect of /two/ multiplications by -1, i.e., of (-1)*(-1)=1.
> 
>    So, a plate of thickness d multiplies by -1.
> 
>    If we combine /two/ plates of thickness d/2 we still get a multipli-
>    cation by -1. So what does /one/ plate of thickness d/2 multiply
>    the amplitude with?
>    

I have a feeling the answer should be /i/, but I'm not sure.  Feel free
to recommend books, websites, or PDF files where I can brush up on light
physics.

-- 
Johann | email: invalid -> com | http://www.myrkraverk.com/blog/
I'm not from the Internet, I just work there. | via Easynews.com