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:

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__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.

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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...

-- KS

*Edited: 25 Sept 2004, 3:30 a.m. *