|[LONG] User-friendly complex-number 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 complex-number 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 single-line entry and a comprehensive menu of relevant functions
- 42S: Provided rectangular or polar modes for entry and calculation, with easy-to-read 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 complex-number functionality. I have yet to see an HP calculator model offer such capability that I consider to be complete and user-friendly. Here's a functional specification of what I believe that would entail:
Convenient one-line 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 48-series models do, the "[+i*]" key could be shifted to enter the angle of a polar-form number. As the 42S and 48-series models do, the angle symbol would be displayed between the components.
The form of a complex number would not change upon entry, unary (one-input) operation, or binary (two-input) operation with scalar. However, rectangular-to-polar and polar-to-rectangular conversions would also change the indicator between "i" and the angle symbol as appropriate.
No parentheses or commas in the display! The tidy 42S-style, representation is preferable to
the messy 28C/S and the 48-series representation of complex-number "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 48-series models do).
Full menu of mathematical operations for complex numbers:
Another single-button 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 complex-valued matrices:
42S-style editing and display of complex-valued matrix elements would be used, although the convenient single-line 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 complex-valued matrices found in the 28C/S, 42S, and 48-series would be included.
Do the high-end TI's (e.,g TI-89) already offer what I have described? Perhaps I should sumbit this to the OpenRPN effort...
Edited: 25 Sept 2004, 3:30 a.m.