Complex number in HP35S


This topic has been discussed in this forum for some time, and I would like to give my experience on that.

First of all, I am not an engineer, and I have never use complex number to solve real world problems. Somebody earlier in this forum recommend an excellent book "the history of the square root of minus one", and so I bought one, and started calculating complex numbers on my 35S.

35S is heritaged from 32SII and 33S, and the complex number support for the latter two calculators are awkward. I originally assumed that it would be equally awkward for the 35S, and surprisingly, it found it very pleasant to use. This is mainly due to the primary button for i. I don't need to care for the limited 4 stacks, and in fact, I think entering complex numbers in 35S is as simple as entering real numbers, and is the easiest among any HP calculators I've used before, including 42S and 48G.

One of the main drawbacks people complain about HP35S (and 32SII and 33S) is its limited complex number support. For example, somebody here said that it should have supported ln(-2), arcsin (2), etc. I don't know, but I just wonder, how many times you would ever need to calculate arcsin (2) in real world problems? Maybe some professionals here need to, then would you please inform me about that.

Best regards,


I think the "how often" justification for not providing a capability misses the point. How often does one calculate the cosine for angles very close to 90 degrees? The HP33S and 35S have documented defects here. Is it not a problem because one seldom performs this function in the affected range? Various natural operations in the real domain generate results in the complex domain for which the HP35S yields no result. I view this as a defect. AT the least it is certainly an avoidable limitation.

The HP42S and the RPL models, and the HP-15C with a little more effort, perform complex number mathematics without user programming. The HP35S and similar do only complex number arithmetic.

The only thing that is required, at the product design phase, to enable the more complete spectrum of capability is a little bit of firmware. It adds no additional weight or power consumption or user complexity.

There is no excuse today, nor for the last 20 years, for any scientific calculator to lack a full capability for complex mathematics.



I agree that the "how often" justification is not a valid justification. If a calculator does something, it ought to do it right, so that is why the cosine bug in the 35s is not acceptable. However I will point out that the 35s does more than simple arithmetic with complex inputs. The following functions accept complex arguments:


Quite a few higher functions in the above list. Not a full suite, of course, but better than just add, subtract, multiply and divide.



While you may be able to take the Ln of a complex function with a calculator, I am eager to ask, does it have a real world meaning?
As an EE I became painfully aware of complex numbers and their manipulation, but it always served a purpose' and had real world application. In 51 we had only manual manipulation which was painful.
with my first calculator HP 35 I discovered relationships not published in books, and I still think they are unknown, as I had tools the book authors did not. Sam


Both the 32S and 35S can compute LN(-2). Arcsin(2) is a bit more complex (excuse the pun), but can be computed on both using the logarithmic form:
arcsin x = -ix*LN(ix+SQRT(1-x^2))


Both the 32S and 35S can compute LN(-2).

My 32sii returns the error message LOG(NEG) /!\.


Perhaps it would be more accurate to say that both the 32S and 35s can compute LN(-2+i0).


Quite so, Jeff. My thoughts were: if you expect an answer in the complex domain ....

For the 32s (& sii is probably the same), use the following key sequence: 0 ENTER 2 +/- SHIFT CMPLX LN. (For complex calcs the Y-register is imaginary part & X-register is the real part).

I totally agree that this is not an easy or ideal way, the 42S implementation is what I would have expected myself on the 35S.


The way to input complex numbers on the 35S is indeed very intuitive and convenient - much better than the 42S and perhaps the best of all HP calcs.

That "i" function sure works great. I wish I could mimic it on the 41 but my MCODE skills are *limited* - say partial key sequence, anyone?

Shame the implementation on the 35S doesn't live up to the same user interface. I love it when on the 42S you get a complex result (instead of an error) when the argument of the function doesn't have a real solution



Complex number entry is great on the 35S, but the limitations in actually working with entered complex numbers is annoying. The inability to decompose a number into its real and imaginary parts is a nuisance. This can be done with a little custom routine, but this sort of stuff should be built-in. Likewise with moving back and forth between polar and rectangular coordinates and the various angular modes. the 42S seems to manage this all so seamlessly. It doesn't have the "i" key, but the COMPLEX function toggles things back and forth and coordinate and angle modes are always respected without hassle.

But I preach to the choir. This stuff has been debated to death since the otherwise pretty good 35S came out two years ago.

Edited: 22 Aug 2009, 4:49 a.m.

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