[LONG] Userfriendly complexnumber calculations Message #1 Posted by Karl Schneider on 25 Sept 2004, 3:27 a.m.
A few of HP's calculator models have introduced useful capabilities for calculating with complex numbers. These include the 15C, the 28C, the 42S, the 48S/SX, and their direct descendants. Other HP models and accessories have provided complexnumber capabilities that are incomplete or downright impractical. These models include the 41C Math Pac, the 20S, and the 32S and 32SII.
Each calculator in the former group has pioneered a good idea:
 15C: Provided complete functionality in the mathematical domain of complex numbers
 28C: Provided straightforward singleline entry and a comprehensive menu of relevant functions
 42S: Provided rectangular or polar modes for entry and calculation, with easytoread full display
 48S/SX: Allowed entry of complex numbers in either form while set in either rectangular or polar mode
However, each of these models had its own shortcomings in regards to complexnumber functionality. I have yet to see an HP calculator model offer such capability that I consider to be complete and userfriendly. Here's a functional specification of what I believe that would entail:
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Convenient oneline entry in either rectangular or polar form:
There should be a "[+i*]" unshifted key that would allow keypad entry of both components of a complex number with only a single extra keystroke. For example, "3.25 [+i*] [+/] 5.64" would display "3.25  i5.64", as the 42S does. The "[+i*]" key would function like "[EEX]", deletable by backarrow to allow correction of the real part.
As the 48series models do, the "[+i*]" key could be shifted to enter the angle of a polarform number. As the 42S and 48series models do, the angle symbol would be displayed between the components.
The form of a complex number would not change upon entry, unary (oneinput) operation, or binary (twoinput) operation with scalar. However, rectangulartopolar and polartorectangular conversions would also change the indicator between "i" and the angle symbol as appropriate.
No parentheses or commas in the display! The tidy 42Sstyle, representation is preferable to
the messy 28C/S and the 48series representation of complexnumber "objects", particularly when these are included within bracketed vector and matrix "objects".
Rectangular or polar mode result setting:
The user could set either a rectagular or polar result mode, which would only determine the form of a binary operation involving one complex number in rectangular form with another in polar form. The mode setting would not automatically change the form of complex numbers in the stack (as the 42S and 48series models do).
Full menu of mathematical operations for complex numbers:
Another singlebutton would bring up a "CMPLX" menu like the one of the 28C/S, offering as a minimum R>C, C>R, R>P, P>R, ABS, CONJ, RE, IM. The SIGN and ARG functions would be optional. Also, RRES and CRES from the 42S could be included.
Complete set of matrix operations for complexvalued matrices:
42Sstyle editing and display of complexvalued matrix elements would be used, although the convenient singleline entry described above would replace the assembly of numbers with the 42S's "CMPLX" function, which incorporates R>C and C>R.
The full functionality for complexvalued matrices found in the 28C/S, 42S, and 48series would be included.
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Do the highend TI's (e.,g TI89) already offer what I have described? Perhaps I should sumbit this to the OpenRPN effort...
 KS
Edited: 25 Sept 2004, 3:30 a.m.
