Cuvee RPN-67 & Complex mode

[Matt Agajanian]

Hi all.

If you’re using RPN-67, how do you use the g OP CPX MODE button? After I press 1 g OP CPX MODE, it seems complex mode should be set. But, when I operate two number functions (+, -, x, /) with complex mode set this way, I get incorrect results.

Please advise on how I use g OP CPX MODE correctly.

Thank you.

[Nigel (UK)]

A brief explanation can be found here (search for CPLX on that page). In short, you can't enter complex numbers onto the stack while you are in complex mode! You have to leave complex mode first, enter the numbers, and then go into complex mode and press whatever buttons you like.

So to multiply (1+2i) by (3+4i) you would:

• Make sure you're not in CPLX mode. If you are, press h CPLX (top left key) to leave it.
• Press 2 ENTER 1 ENTER 4 ENTER 3 (don't press ENTER here)
• Press h CPLX to turn on complex mode (don't use g OP 1), and then press \(\times\).
• The display now shows the real part of the result (-5 in this case); press x<>y to see the imaginary part.
  

If you now want to enter another complex number you have to leave complex mode. At least, I can't see how to enter complex numbers while in complex mode! (I tried using x<>y to separate real and imaginary parts, but it doesn't work: when the imaginary part of the new complex number is entered, the T register changes.)

Note that using g OP 1 to enter and leave complex mode isn't the way to go, as this consumes the contents of the x-register.

Well, you wouldn't want it to be easy and/or intuitive, would you? If it were, anyone could use it!

(Apologies if I'm overlooking something simple here.)

Nigel (UK)

[Matt Agajanian]

Thank for the explanation. I do understand how to use h CPLX. Yes, that’s pretty straightforward.

But, to me it doesn’t make sense that once you’re in complex mode, shouldn’t that mean 3+4i x 9+5i is entered as.

3 ENTER
4 ENTER
9 ENTER
5 ENTER X

since complex mode is active?

But, I'm still puzzled about the 1 g OP CPLX MODE function.

I could see the checking mode operation as
(n<> 0 and n<>1) g OP CPX MODE.

But, why wouldn’t activating Complex Mode first with 1 g OP CPX MODE and then to evaluate 3+4i x 9+8i entering 3 ENTER 4 ENTER 9 ENTER 8 X would reveal the real component in X and imaginary component would be in Y.

In other words, shouldn’t 1 g OP CPX MODE already be sufficient to set up complex mode?

(10-14-2022 02:45 PM)Nigel (UK) Wrote:  A brief explanation can be found here (search for CPLX on that page). In short, you can't enter complex numbers onto the stack while you are in complex mode! You have to leave complex mode first, enter the numbers, and then go into complex mode and press whatever buttons you like.

So to multiply (1+2i) by (3+4i) you would:

• Make sure you're not in CPLX mode. If you are, press h CPLX (top left key) to leave it.
• Press 2 ENTER 1 ENTER 4 ENTER 3 (don't press ENTER here)
• Press h CPLX to turn on complex mode (don't use g OP 1), and then press \(\times\).
• The display now shows the real part of the result (-5 in this case); press x<>y to see the imaginary part.
  

If you now want to enter another complex number you have to leave complex mode. At least, I can't see how to enter complex numbers while in complex mode! (I tried using x<>y to separate real and imaginary parts, but it doesn't work: when the imaginary part of the new complex number is entered, the T register changes.)

Note that using g OP 1 to enter and leave complex mode isn't the way to go, as this consumes the contents of the x-register.

Well, you wouldn't want it to be easy and/or intuitive, would you? If it were, anyone could use it!

(Apologies if I'm overlooking something simple here.)

Nigel (UK)

[Nigel (UK)]

The problem is that in complex mode pressing ENTER copies both the X and Y registers into Z and T, so you can’t enter numbers one at a time. I tried to enter numbers in complex mode using x<>y, like this:
4 x<>y 3 ENTER 5 x<>y 9 MULTIPLY
But when the final 9 is pressed, the 5 in Y is copied into T!

It helps to have the stack contents display visible while experimenting. It is then very clear when something isn’t working!

Nigel (UK)

[Matt Agajanian]

(10-15-2022 12:03 PM)Nigel (UK) Wrote:  The problem is that in complex mode pressing ENTER copies both the X and Y registers into Z and T, so you can’t enter numbers one at a time. I tried to enter numbers in complex mode using x<>y, like this:
4 x<>y 3 ENTER 5 x<>y 9 MULTIPLY
But when the final 9 is pressed, the 5 in Y is copied into T!

It helps to have the stack contents display visible while experimenting. It is then very clear when something isn’t working!

Nigel (UK)

Thanks. So, outside of testing the setting with

x (other than 0 or 1) g OP CPX MODE to see or test the setting, what’s the purpose of

setting or clearing Complex mode with the g OP CPX MODE operation?

[Nigel (UK)]

I think that g OP CPX MODE would be useful in a program, to establish definitely that complex mode is turned on or off at the start. CPLX can then be used to toggle as needed.

Nigel (UK)

[Matt Agajanian]

I’m thinking of this as another workaround:

12+40i x 61+50i

12 ENT 40 ENT
61 ENT 1 g OP CPX MODE
CLx
50 x

Just a little additional step, but it gets the correct calculation.

[Willy R. Kunz]

As the author of RPN-67, let me put my two cents in.

Complex mode was designed as a convenient utility for doing quick evaluations of operations and functions involving complex numbers. It doesn't turn RPN-67 into a complex numbers calculator.

RPN-45, on the other hand, sports a "real" complex mode, complete with 4-level stack and unrestricted register arithmetic. If high-contrast mode is on, you can even see the the full complex result with both real and imaginary parts. To input 2+3i, for example, you would type 2 ENTER 3 I, without losing any stack level (except the complex number in T, of course).

   

[Nigel (UK)]

Thank you for this perspective. As well as RPN-67 I also own RPN-45, 70, and 97 so I'm certainly a fan of your work! To be honest I'd never looked at the RPN-67 complex mode before reading Matt's post about it; I was a little surprised at what it was like, given how complex mode is implemented in RPN-45, but that's fine. There's nothing wrong with being different. All of these calculators look great and work brilliantly!

Incidentally, the following key sequence allows the calculation of (1+2i) x (3+4i) on RPN-67 entirely within complex mode:

• Make sure complex mode is active;
• Press 2 x<>y 1 ENTER 4 x<>y CLx 3 x.
  

This leaves -5 in X and 10 in Y, as it should. The CLx disables stack lift and allows the 3 to be entered without changing Z and T.

Nigel (UK)

[Matt Agajanian]

SNIP

(10-19-2022 04:37 PM)Nigel (UK) Wrote:  Incidentally, the following key sequence allows the calculation of (1+2i) x (3+4i) on RPN-67 entirely within complex mode:

• Make sure complex mode is active;
• Press 2 x<>y 1 ENTER 4 x<>y CLx 3 x.
  

This leaves -5 in X and 10 in Y, as it should. The CLx disables stack lift and allows the 3 to be entered without changing Z and T.

Nigel (UK)

SNIP.

That’s an improvement compared to my method. It looks like I’ll be using your method instead. Thanks!

[Willy R. Kunz]

(10-19-2022 04:37 PM)Nigel (UK) Wrote:  Thank you for this perspective. As well as RPN-67 I also own RPN-45, 70, and 97 so I'm certainly a fan of your work! To be honest I'd never looked at the RPN-67 complex mode before reading Matt's post about it; I was a little surprised at what it was like, given how complex mode is implemented in RPN-45, but that's fine. There's nothing wrong with being different. All of these calculators look great and work brilliantly!

Incidentally, the following key sequence allows the calculation of (1+2i) x (3+4i) on RPN-67 entirely within complex mode:

• Make sure complex mode is active;
• Press 2 x<>y 1 ENTER 4 x<>y CLx 3 x.
  

This leaves -5 in X and 10 in Y, as it should. The CLx disables stack lift and allows the 3 to be entered without changing Z and T.

Nigel (UK)

Correct. I was just going to suggest this method, when I noticed your post.

Incidentally, the next version will have a new Extra Function (number 16) called Toggle CPLX Mode. It will simply turn complex mode on or off.
So you store 16 in the FN register, then execute g OP EXEC FN to toggle complex mode. The stack remains unaffected.
For convenience, you may even add a 3-step program:

Code:

LBL C
OP EXEC FN
RTN

which allows you to turn complex mode on and off by simply pressing C.