E**(i*pi)=-1 or e**(j*pi)=-1, something I found out in Python using part of Eulers Identit equation. Post: 303042083

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Top Forums Programming E**(i*pi)=-1 or e**(j*pi)=-1, something I found out in Python using part of Eulers Identit equation. Post 303042083 by wisecracker on Friday 13th of December 2019 01:54:58 PM

12-13-2019

Registered User

E**(i*pi)=-1 or e**(j*pi)=-1, something I found out in Python using part of Eulers Identit equation.

Well guys and gals I have discovered after all these years that Python does complex numbers without the 'complex()' function or 'cmath' import.
It is well known that Euler's Identity E**(i*pi)+1=0 so I decided to experiment

Code:

Last login: Fri Dec 13 18:27:30 on ttys000
AMIGA:amiga~> python3.8
Python 3.8.0rc1 (v3.8.0rc1:34214de6ab, Oct  1 2019, 12:56:49) 
[Clang 6.0 (clang-600.0.57)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> pi=3.14159265359
>>> e=2.71828182846
>>> 
>>> e**(pi*1j)
(-1-1.31038479358762e-12j)
>>> exit()
 AMIGA:amiga~> _

As you can see within the limitations of the floating point accuracy e**(pi*1j)=-1.
We all live and learn and it also works for Python 1.4.0 for the AMIGA.

Last edited by wisecracker; 12-13-2019 at 03:02 PM.. Reason: Added last two lines.

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IDLE(1) 						      General Commands Manual							   IDLE(1)

NAME

       IDLE - An Integrated DeveLopment Environment for Python

SYNTAX

       idle [ -dins ] [ -t title ] [ file ...]

       idle [ -dins ] [ -t title ] ( -c cmd | -r file ) [ arg ...]

       idle [ -dins ] [ -t title ] - [ arg ...]

DESCRIPTION

       This  manual page documents briefly the idle command.  This manual page was written for Debian because the original program does not have a
       manual page.  For more information, refer to IDLE's help menu.

       IDLE is an Integrated DeveLopment Environment for Python. IDLE is based on Tkinter, Python's bindings to the Tk widget  set.  Features  are
       100%  pure  Python, multi-windows with multiple undo and Python colorizing, a Python shell window subclass, a debugger. IDLE is cross-plat-
       form, i.e. it works on all platforms where Tk is installed.

OPTIONS

       -h     Print this help message and exit.

       -n     Run IDLE without a subprocess (see Help/IDLE Help for details).

       The following options will override the IDLE 'settings' configuration:

       -e     Open an edit window.

       -i     Open a shell window.

       The following options imply -i and will open a shell:

       -c cmd Run the command in a shell, or

       -r file
	      Run script from file.

       -d     Enable the debugger.

       -s     Run $IDLESTARTUP or $PYTHONSTARTUP before anything else.

       -t title
	      Set title of shell window.

       A default edit window will be bypassed when -c, -r, or - are used.

       [arg]* and [file]* are passed to the command (-c) or script (-r) in sys.argv[1:].

EXAMPLES

       idle   Open an edit window or shell depending on IDLE's configuration.

       idle foo.py foobar.py
	      Edit the files, also open a shell if configured to start with shell.

       idle -est "Baz" foo.py
	      Run $IDLESTARTUP or $PYTHONSTARTUP, edit foo.py, and open a shell window with the title "Baz".

       idle -c "import sys; print sys.argv" "foo"
	      Open a shell window and run the command, passing "-c" in sys.argv[0] and "foo" in sys.argv[1].

       idle -d -s -r foo.py "Hello World"
	      Open a shell window, run a startup script, enable the debugger, and run foo.py, passing "foo.py" in sys.argv[0] and "Hello World" in
	      sys.argv[1].

       echo "import sys; print sys.argv" | idle - "foobar"
	      Open a shell window, run the script piped in, passing '' in sys.argv[0] and "foobar" in sys.argv[1].

SEE ALSO

       python(1).

AUTHORS

       Various.

								 21 September 2004							   IDLE(1)