Complex number capability in nonHP machines Message #1 Posted by Palmer O. Hanson, Jr. on 5 July 2008, 11:13 p.m.
In a May 17 thread "HP 35s successor?" Rodger Rosenbaum asked:
Quote:
Has there ever been a nonHP calculator with excellent complex number capability?
The ones I've seen have been abysmal.
Since no one else has responded to Roger's question with respect to nonHP calculators I decided to try. My answer is limited to machines to which I have access. I wrote separately to Rodger noting that several machines in the TI product line had what I thought were substantial complex number capabilities. He responded
Quote:
I have a TI86, and as you say, it has comprehensive complex variable
capability. But, my experience with calculators other than HP or TI
has been that if they have any complex capability at all, it is rudimentary.
My Casio fx115D offers the four arithmetic functions and 1/x.
My Casio fx115ES (currently available) offers the four arithmetic functions, 1/x, x^2, x^3, argument and conjugate.
My Sharp EL515S has a complex mode which offers only the four arithmetic functions.
My Sharp PC1261 Pocket Computer does not offer a builtin complex capability. The PC1260/1261 Instruction Manual includes fifteen sample programs none of which provide complex number capabilities. Sharp's Application Software for PC1250/CE125 includes twenty BASIC programs. Again, none of them provide complex number capabilities. The book Mathematics Library  Application Software for the Sharp EL5500 and PC1403 Scientific Computers by Maurice E. T. Swinnen and David Thomas (Systems Publications, 1987) offers five BASIC programs for complex number calculations:
Program 1. Sine, cosine and tangent and the inverses.
Program 2. The four arithmetic functions plus polar to rectangular and rectangular to polar conversions.
Program 3. Square, square root, reciprocal, natural log, e^x, plus polar to rectangular and rectangular conversions.
Program 4. y^x, y^(1/x), log to the base y of x, plus polar to rectangular and rectangular to polar conversions.
Program 5. Complex Roots
These programs should be compatible with the PC1261. I have successfully run parts of the first three on my PC1261. I have successfully run the Simultaneous Equation program from the book on my PC1261 and converted it for use with my Radio Shack Model 100 and with my Texas Instruments CC40.
The book provides example calculations which can be used to verify that the programs have been entered correctly. For the first program the sine of 3  5i is calculated as 3.883848618 74.10151768i which does NOT agree with the result obtained with my TI85 and HP28S. The first line of the program sets degree mode. If I set radian mode instead I get results which agree with my TI85 and HP28S. Degree mode is also set at the beginning of programs 3 and 4. As a result the example calculation for any function which uses real trigonometric functions as a part of its solution will not agree with results from machines which use radian mode. Setting radian mode will result in agreement. I leave any discussion over the merits of the use of degree or radian mode to others more skilled in the use of complex functions than I am.
To demonstrate the arcsine fnction the book asks the user to enter 3.8838  74.1i (a truncated version of the sine of 3  5i when using degree mode) and see 3.000023834  4.99997943i as the answer. There is a better way to demonstrate the arcsine after having calculated the sine. The input routine stores the real part in R and the imaginary part in M. Each complex trigonometric function stops with the real part in O and the imaginary part in P. Since the PC1261 accepts variables as the response to INPUT statements the user can enter the complete answer from a previous trigonometric function by responding with O and P for the real and imaginary inputs. A user who does that to calculate the arcsine after having calculated the sine of 3  5i in degree mode will see the result 3.000000101  4.999999881 .
The arithmetic functions in the second program stop with the result in the locations where the first complex number is entered for an arithmetic function. The INPUT statement of the PC1261 does not display those values; however, if ENTER is pressed the INPUT statement essentailly acts as a nonoperation and the existing values in the input locations are preserved. The INPUT statement on my Radio Shack Model 100 reacts in the same way. To preserve the previously stored values on the CC40 the user must use the response Shift ENTER.
I have not worked with the fifth program.
The TI Machines:
Rodger noted that the TI86 has a comprehensive capability. Several other TI machines also offer comprehensive capability.
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The TI58/58C/59 offer complex calculations if either the Master Library module or the Electrical Engineering module is in place. Three subprograms offer the four arithmetic functions, x^2, square root, 1/x, e^x, ln x and sin, cos, tan and the
inverses. The functions are selected from subprograms with the user defined keys (A through E and A' through E'). Prompting to the display is not available since the TI59 does not offer alphanumerics in the display. The user can use the label card in the slot above the top row of keys. That requires shuffling the appropriate cards in and out of the slot. Frank Fujimoto recognized the various limitations of that method and wrote a Complex Keyboard program which was published in the Volume 4 Number 4 (July/August 1980) issue of PPX Exchange. His program offers access to all of the complex functions in the memory module. Seven complex memory registers are provided which can be accessed with Store, Recall, Exchange, Sum, Inverse Sum, Product and Inverse Product functions. I recommend that the user change step 026 of the program from B to INV and step 117 of the program from INV to B. Then the user can perform complex mathematics with the same keyboard sequences that would be used for real functions except that SBR must be pressed before each complex function.
The CC40, the TI74 and the TI95 all offer an extended capability as part of their Mathematics Library modules including x^2, SQRT, 1/x, LN, EXP, SIN, COS, TAN, ASIN, ACOS, ATAN, y^x and x root of y. The CC40 and the TI95 also offer LOGyX. The TI74 does not. A curious addendum to the TI74 manual states:
Quote:
The Complex Functions Program (COMPF) contains two complex logarithm options, LN(X) and LOGyX . LOGyX calculations are needed less often than LN(X) calculations. To prevent you from accidentally selecting LOGyX when you intend to calculate LN(X), th LOGyX option (Option 20) has been disabled. Selecting this option results in an 'E1 Syntax' error message.
The addendum then goes on to offer a program to calculate LOGyX. Somehow, I believe that a user of the complex capability will be able to keep track of which function to use.
The TI95 also offers the hyperbolics and their inverses. The CC40 and the TI74 offer a Complex Systems program (COMPS) which solve a system of nxn simultaneous equations with complex coefficients. The baseline 6K versions of the machines will handle up to 12x12 complex systems. The program is easy to use with excellent prompting.
The first page of the section on complex numbers in the TI68 Guidebook states: "A major innovation of the TI68 is its extensive complex number capability. You have the freedom to enter complex numbers wherever they are applicable without 'mode' limitations. Few other calculators evn approach the versatility of complex numbers provided by the TI68." How much salesmanship and how much actual capability? I haven't done any substantial amount of work with the TI68. I do know that the method of entering and displaying is similar to the HP48. I can't compare with the HP15 or the HP42 since I don't have either of those.
Many of the TI graphic machines offer complex number capabilities. The TI83 offers a relatively wide range of functions but it does not offer the trigonometric functions. I have not tested my TI84. The TI85 offers all the capabilites of the TI83 and adds the trigonometric and hyperbolic functions and their inverses, polynomial solutions, simultaneous equation solutions, sorting based on modulus, and the sum or product of the elements of a list.
A Question on HP Capabilities
I haven't been able to use memory register arithmetic with complex functions in Algebraic mode on the HP35S. I haven't found a reference in the manual which indicates that should be so. I may be doing something incorrectly. If anyone knows how to do that please let me know.
