Complex Powers & Roots on RPN-67

[Matt Agajanian]

Hi all.

I’m sure you’re familiar with or have used Cuvee Software’s RPN-67.

Let’s say you have (11+2i)^4.


So, it would seem this is the correct entry:

CPLX mode is off
h RAD
11 ENTER
2 ENTER
4 ENTER
0
h CPLX (turns Complex Mode on)
h y^x

This seems the logical process, but I get:

Z
T
Y -0.0009
X -0.0037

Clearly not

Z
T
Y 10296
X 11753
Which is the correct value.
What am I missing?

[Nigel (UK)]

For each number you need to enter its imaginary part first.

Nigel (UK)

[Matt Agajanian]

(01-06-2023 09:22 AM)Nigel (UK) Wrote:  For each number you need to enter its imaginary part first.

Nigel (UK)

Thanks for the tip. Just curious,

With the real number range, 3^5 would be entered as 3 ENTER 5 *. So why would complex numbers need to be entered in reverse (3+5i as 5 [5 ENTER 3 ENTER])?

[Nigel (UK)]

(01-06-2023 08:05 PM)Matt Agajanian Wrote:  

(01-06-2023 09:22 AM)Nigel (UK) Wrote:  For each number you need to enter its imaginary part first.

Nigel (UK)

Thanks for the tip. Just curious,

With the real number range, 3^5 would be entered as 3 ENTER 5 *. So why would complex numbers need to be entered in reverse (3+5i as 5 [5 ENTER 3 ENTER])?

It's normal to write a complex number as \(x+{\rm i}y\). So, on an RPN calculator, it seems natural to have \(x\) - the real part - in the X register, and \(y\) - the imaginary part - in the Y register. To make this work, you have to enter Y and then X. The good this is that when you get your answer, what is in the display - the X register - is the real part of the answer, which I think is what you should see first.

Many other RPN calculators work in this way. (The 42S is an exception - there may be others?)

Nigel (UK)

[Matt Agajanian]

(01-06-2023 09:22 AM)Nigel (UK) Wrote:  For each number you need to enter its imaginary part first.

Nigel (UK)

Thanks for the tip. Just curious,

With the real number range, 3^5 would be entered as 3 ENTER 5 y^x. So why would complex numbers need to be entered in reverse (3+5i as 5 [5 ENTER 3 ENTER])?

[Thomas Klemm]

(01-06-2023 10:03 PM)Nigel (UK) Wrote:  Many other RPN calculators work in this way. (The 42S is an exception - there may be others?)

HP-15C

11 ENTER 2 I
4 \(y^x\)

11,753.0000

Re<>Im

10,296.0000


HP-48G

11 ENTER 2 R->C
4 ^

(11753,10296)

Which HP calculator did you have in mind?

[Nigel (UK)]

(01-06-2023 11:47 PM)Thomas Klemm Wrote:  

(01-06-2023 10:03 PM)Nigel (UK) Wrote:  Many other RPN calculators work in this way. (The 42S is an exception - there may be others?)

HP-15C

11 ENTER 2 I
4 \(y^x\)

11,753.0000

Re<>Im

10,296.0000


HP-48G

11 ENTER 2 R->C
4 ^

(11753,10296)

Which HP calculator did you have in mind?

OK, it was late when I wrote the above - I overgeneralised from the HP32SII and HP33S (which do handle complex numbers in this "backwards" way, I believe) and from the WP34S - not a HP machine, I admit, but then the HP-48G isn't (strictly) RPN!

Thank you for the correction.

Nigel (UK)

[Nigel (UK)]

(01-06-2023 11:27 PM)Matt Agajanian Wrote:  

(01-06-2023 09:22 AM)Nigel (UK) Wrote:  For each number you need to enter its imaginary part first.

Nigel (UK)

Thanks for the tip. Just curious,

With the real number range, 3^5 would be entered as 3 ENTER 5 y^x. So why would complex numbers need to be entered in reverse (3+5i as 5 [5 ENTER 3 ENTER])?

To be clear: to work out (1+2i)^(3+4i) you would enter (on the RPN-67 and similar machines):

2 ENTER 1 ENTER 4 ENTER 3 y^x.

At least, I think so. Try it and see!

Nigel (UK)

[toml_12953]

(01-06-2023 11:27 PM)Matt Agajanian Wrote:  

(01-06-2023 09:22 AM)Nigel (UK) Wrote:  For each number you need to enter its imaginary part first.

Nigel (UK)

Thanks for the tip. Just curious,

With the real number range, 3^5 would be entered as 3 ENTER 5 y^x. So why would complex numbers need to be entered in reverse (3+5i as 5 [5 ENTER 3 ENTER])?

Because the y^x key takes whatever is in the y register and raises it to the x power. For 3^5, the 3 would be the y and the 5 would be the x.

When we think of pairs of numbers such as coordinates, we usually think of (x,y) pairs. The real part comes first in an imaginary number so it goes in x and the imaginary part goes in y. In 3^5, 3 and 5 are not considered a pair of numbers, they're just two separate numbers.

[Albert Chan]

RPN turned infix operator to postfix: 3 ^ 5 --> 3 5 [^]

Complex number normally expressed as (a + i*b), not (b*i + a)
We can think of [+i*] as an operator: 3 +i* 5 --> 3 5 [+i*]

It is more intuitive to input real part first, imaginery part second.
Perhaps that's why the switch over ... my 2¢

[Matt Agajanian]

(01-07-2023 01:49 PM)Albert Chan Wrote:  RPN turned infix operator to postfix: 3 ^ 5 --> 3 5 [^]

Complex number normally expressed as (a + i*b), not (b*i + a)
We can think of [+i*] as an operator: 3 +i* 5 --> 3 5 [+i*]

It is more intuitive to input real part first, imaginery part second.
Perhaps that's why the switch over ... my 2¢

I agree. Although the reverse is true for RPN-67, the more I use its method of entering complex numbers, the more it makes sense to me. Even so, your idea also makes sense to me.