Calculator test
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12-06-2024, 10:27 PM
Post: #1
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Calculator test
Hi Ladies and Gents,
Euler, in the 18th century wrote down a very important equation, this being in one form can be written: e^(pi.i)=cos(pi)+i.sin(pi) which equates to e^(pi.i)=-1 Which can be written as e^(pi.i)+1=0 Know we can also deduce that pi.i=ln(-1) Key in ln(-1) into your best calculator and hit return, your calculator should give pi.i, if it throws up a domain error try putting into complex rectangular mode and try again. As expected, my hp15ce and ti30x pro mp throws up error 0, which didn't surprise me. Cheers Darren TI89T,TI83+,TI84+,TI84+SE,TI84+C,TI84+CE, TI30X-MP,HP50g,HP45,HP15CE,HP35s,Casio cg50,Casio 991cw |
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12-06-2024, 11:19 PM
(This post was last modified: 12-10-2024 12:23 AM by Steve Simpkin.)
Post: #2
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RE: Calculator test
I must admit that I am surprised that the HP-15C shows an error for this. I thought it would provide a complex answer like the HP-42S. The oldest HP I have that can answer this is the HP-28C, as do all of the RPL machines. The oldest TI I have that provides an answer is the TI-92 (symbolic πi). The TI-84 Plus returns an answer if it is set for complex answers. The HP 35s returns a "LOG(NEG)" error.
Edit: Other have confirmed the the HP-15C will produce a complex answer if it is set to complex mode first (SF 8). Edit 2: The HP 35s does return an answer to LN(-1) if the argument is complex. For example LN(-1i0) = 0i3.14159265359. |
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12-06-2024, 11:20 PM
(This post was last modified: 12-07-2024 12:15 AM by Johnh.)
Post: #3
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RE: Calculator test
That's very interesting, a new insight for me. I hadn't realised there was such a relationship between Pi, natural logs and complex numbers.
Hp15c-ce actually does do it! Need to set to complex mode first (SF 8), then do LN of -1 and it displays 0 as the real part, and the imaginary part is displayed as Pi by revealing it with (i). On a few emulators for Hp15c such as TouchRPN, JRPN 15 and Pockemul, it works the same. And Free42 and Plus42 display it directly. I'm not sure about Hp35s. I have this but never spent time with its complex mode. But it doesn't seem to do it in its default mode.and puts up a LOG(NEG) message. |
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12-06-2024, 11:31 PM
(This post was last modified: 12-06-2024 11:41 PM by naddy.)
Post: #4
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RE: Calculator test
I'm not sure what the point of the exercise is. Obviously, there are three possibilities:
The prototypical test for complex support would be \(\sqrt{-1}\). The best calculator is the one you actually use. |
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12-07-2024, 03:33 AM
Post: #5
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RE: Calculator test
(12-06-2024 11:19 PM)Steve Simpkin Wrote: I thought it would provide a complex answer like the HP-42S. Complex results for real-number operations can be disabled with REALRES. This function sets flag 74. Example -1 LN Invalid Data But it still works for a complex number: -1 i0 LN 0 i3.14159265359 It can be enabled with CPXRES. This function clears flag 74 (default). |
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12-07-2024, 03:34 AM
Post: #6
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RE: Calculator test
(12-06-2024 10:27 PM)Commie Wrote: Hi Ladies and Gents, Is the notation used here "xyz.i" some kind of standard shorthand for "xyz*i" ? Not saying it's bad or wrong, I'm just not familiar with it. Where is it from? --Bob Prosperi |
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12-07-2024, 08:49 AM
(This post was last modified: 12-07-2024 09:04 AM by StephenG1CMZ.)
Post: #7
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RE: Calculator test
I have seen that notation used before, though the "." is meant to be level with the characters rather than lower down.
https://en.m.wikipedia.org/wiki/Multipli...erminology Apparently it was introduced by Leibniz in 1689: https://jeff560.tripod.com/operation.html Ànd it was occasionally seen in India before that. Stephen Lewkowicz (G1CMZ) https://my.numworks.com/python/steveg1cmz |
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12-07-2024, 09:47 AM
(This post was last modified: 12-07-2024 11:11 AM by Idnarn.)
Post: #8
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RE: Calculator test
(12-06-2024 10:27 PM)Commie Wrote: Key in ln(-1) into your best calculator and hit return, your calculator should give pi.i, if it throws up a domain error try putting into complex rectangular mode and try again.
In the case of Casios:
A more interesting test of complex numbers support is trying trigonometry on complex numbers. The HP 15C CE performs sin(), cos(), tan() of complex numbers. All of the fore-mentioned Casio calculators don't have any support for these functions on complex numbers. It's unexpected that Casio in this age still doesn't support it esp. on the latter two calculators that support complex numbers as it'd be trivial to implement considering everything else these calculators do. The fx-CG50 has the KhiCAS (xcas/giac) addon though which kinda makes up for it. |
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12-07-2024, 10:32 AM
Post: #9
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RE: Calculator test
(12-06-2024 11:20 PM)Johnh Wrote: Hp15c-ce actually does do it! Need to set to complex mode first (SF 8), then do LN of -1 and it displays 0 as the real part, and the imaginary part is displayed as Pi I just want to confirm Johnh and others are correct, the hp15ce does indeed work and gives the correct answer in complex mode. This is quite amazing given that the hp15c debut in 1982. Cheers Darren TI89T,TI83+,TI84+,TI84+SE,TI84+C,TI84+CE, TI30X-MP,HP50g,HP45,HP15CE,HP35s,Casio cg50,Casio 991cw |
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12-07-2024, 01:14 PM
Post: #10
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RE: Calculator test
(12-07-2024 08:49 AM)StephenG1CMZ Wrote: I have seen that notation used before, though the "." is meant to be level with the characters rather than lower down. Sure, I've seen dotted notation with a dot symbol for multiplication but as you say that dot is vertically centered on the characters, just as "*", "+", "-", etc. are. I've never seen the period used in this way?? --Bob Prosperi |
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12-07-2024, 01:22 PM
(This post was last modified: 12-07-2024 01:29 PM by AnnoyedOne.)
Post: #11
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RE: Calculator test
In my PC Hewlett Packard HP-15C emulator (with the 192 register patch)
https://www.hpmuseum.org/forum/thread-22453.html I activated complex mode (g SF 8), entered -1, then g Ln and got 0 f Re<>Im gave 3.1416 which I believe is 0 + pi.i = pi.i In real (non-complex) mode I got "Error 0" which is correct. Of course you have to know that the result of Ln(-1) is complex just as the designers did. Read "Section 3: Calculating in Complex Mode" of the Advanced Functions Handbook (AFH), Ln(z), [page 70 in the original book]. A1 HP-15C (2234A02xxx), HP-16C (2403A02xxx), HP-15C CE (9CJ323-03xxx), HP-20S (2844A16xxx), HP-12C+ (9CJ251) |
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12-07-2024, 07:17 PM
Post: #12
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RE: Calculator test
I grew up in the UK, with high-school maths in the 1970's.
I often use the "." in the lower position to denote multiplication, but only for algebraic descriptions such as a = b.c . As with other english-speaking countries, we also use "." as the decimal point, so with numbers it has to be an explicit × or x eg 2 × 3 = 6 at least for me. And if it's code or excel, a "*' is used. But who taught me that use of the period "." ? Did I learn maths wrongly? or should I start a class action in my old maths class? |
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12-07-2024, 07:23 PM
(This post was last modified: 12-07-2024 07:31 PM by AnnoyedOne.)
Post: #13
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RE: Calculator test
(12-07-2024 07:17 PM)Johnh Wrote: I often use the "." in the lower position to denote multiplication... I learnt it as "dot product" for vector multiplication (bigger dot). https://en.wikipedia.org/wiki/Dot_product That said, on the internet etc, I've seen *, x, and . used. Some have browser extensions etc to enter mathematical symbols but I (and others) usually don't bother. A1 HP-15C (2234A02xxx), HP-16C (2403A02xxx), HP-15C CE (9CJ323-03xxx), HP-20S (2844A16xxx), HP-12C+ (9CJ251) |
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12-07-2024, 07:50 PM
Post: #14
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RE: Calculator test
Interesting thread!
What I remember from school: HP 41C/CX/CL at work. The rest for playtime! |
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12-07-2024, 08:11 PM
Post: #15
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RE: Calculator test
(12-07-2024 03:34 AM)rprosperi Wrote:(12-06-2024 10:27 PM)Commie Wrote: Which can be written as e^(pi.i)+1=0 As the Wikipedia article explains: Quote:Historically, in the United Kingdom and Ireland, the middle dot was sometimes used for the decimal to prevent it from disappearing in the ruled line, and the period/full stop was used for multiplication. The best calculator is the one you actually use. |
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12-07-2024, 08:12 PM
(This post was last modified: 12-07-2024 08:14 PM by JurgenRo.)
Post: #16
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RE: Calculator test
(12-07-2024 07:50 PM)Geoff Quickfall Wrote: Interesting thread! I am a mathematician, but I have never seen A(B) as a product. A(B) is rather a common abbreviation for “A is a function of B”. On the other hand you missed AB, which is very common and called "implicit notation" for A*B. In general, the meaning of a product is derived from the context. Ambiguities (scalar product, vector product) therefore generally have special notations (A x B: vector product, cross product; <A,B>: scalar product etc.). Edit: typo |
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12-07-2024, 08:20 PM
Post: #17
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RE: Calculator test
Your correct, forgot about the AB form.
The A(B) should really have been described as: A(B +C) to imply priority and the A(B) was incorrect as the parentheses are redundant in a strictly multiplicational (word?) aspect. Did say, from memory :-) Cheers HP 41C/CX/CL at work. The rest for playtime! |
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12-07-2024, 08:23 PM
Post: #18
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RE: Calculator test
(12-07-2024 08:12 PM)JurgenRo Wrote: ... Oh no, the dreaded Implicit Multiplication Calculator Conundrum! Order of operations - what is 6÷2(1+2) ? See also: https://sites.google.com/view/hp-plus-ca...rehj3fwg80 |
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12-07-2024, 08:23 PM
(This post was last modified: 12-07-2024 08:29 PM by Commie.)
Post: #19
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RE: Calculator test
Hi Guys,
Just wanna point out, for those calculators that do work, it doesn't have to be fixed at ln(-1), you can use any negative number which can deliver a real and a complex number. For example, ln(-0.5)=-0.69+pi.i I've checked my hp15ce and yes it works, I'm growing to like my 15ce! Cheers Darren TI89T,TI83+,TI84+,TI84+SE,TI84+C,TI84+CE, TI30X-MP,HP50g,HP45,HP15CE,HP35s,Casio cg50,Casio 991cw |
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12-08-2024, 07:36 AM
(This post was last modified: 12-08-2024 07:49 AM by C.Ret.)
Post: #20
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RE: Calculator test
(12-06-2024 10:27 PM)Commie Wrote: Key in \(ln(^-1)\) into your best calculator and hit return, your calculator should give \(\pi\cdot i\) Hi Commie, your best calculators have a RETURN key ? (12-07-2024 03:33 AM)Thomas Klemm Wrote:(12-06-2024 11:19 PM)Steve Simpkin Wrote: I thought it would provide a complex answer like the HP-42S.Complex results for real-number operations can be disabled with REALRES. This function sets flag 74. This observation exactly match how the HP-15C works, except there is no specific command apart setting Flg 8 which is the complex-mode toggle or indicator. (12-07-2024 01:22 PM)AnnoyedOne Wrote: I activated complex mode (g SF 8), entered -1, then g Ln and got Right. There is an alternative way of promoting complex mode on the HP-15C; it is simply to enter arguments as complex number. So the same observation can be made, from 'standard' calculator state (the state we get after a reset [ON]+[ - ] ). In 'real entry mode', results are strictly real: [ 1 ][CHS][g][ LN ] display Error 0. In 'extended complex stack mode', using one of the many entry methods: [ 1 ][CHS][ENTER][ 0 ][f][ I ][g][ LN ] set the flag 8 and display real part 0.0000 and [f][(i)] or [f][Re⇋Im] display imaginary part 3.1416. Unfortunately, there is no other way to quit the complex extend mode than clearing flag 8 by [f][ CF ][ 8 ] or by resetting the calculator. Note, that trying the equation \(e^{\pi\cdot i}=^-1\) the opposite direction, show an interesting fact (or flow) about HP-15C precision in complex computations: [g][ ∏ ][f][Re⇋Im][ ◀- ][ e^x ] exactly display real part -1.0000 but the imaginary part is not exactly what we expect; [f][(i)] or [f][Re⇋Im] display 4.1000 -10. (12-07-2024 08:23 PM)Commie Wrote: I've checked my hp15ce and yes it works, I'm growing to like my 15ce! Really Commie? Even is there is no RETURN key on our beloved device? |
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