HP50G Complex Number CAS manipulations
04-07-2015, 06:24 PM
Post: #1
 Hammonds Junior Member Posts: 3 Joined: Apr 2015
HP50G Complex Number CAS manipulations
In page 22 of the Complex Numbers with the HP49G marathon PDF, the author states:

Quote:Let's suppose, we have the equation
z^2 − z = 0 and we want to solve for z, which is complex. Using ABS
we find that the absolute value of z^2 − z is:

The answer given is a long statement of the form
sqrt(RE(Z)^4− 2RE(Z)^3+2(IM(Z)^2+1) ...etc)

My question is how is he getting the CAS to expand the original equation in this way? The most that happens for me is that I get absolute value symbols "||" placed around the z^2 - z. I have tried several combinations of CAS settings, but to no avail.

Can someone help me with the settings and key sequence? I am using an HP50G.

Thanks.
04-07-2015, 07:03 PM (This post was last modified: 04-07-2015 07:04 PM by Gerald H.)
Post: #2
 Gerald H Senior Member Posts: 1,458 Joined: May 2014
RE: HP50G Complex Number CAS manipulations
Are you in complex mode? Is the C annunciator showing or R?

Set complex with HOLD LEFT SHIFT & I.

ABS should then work as you want.
04-07-2015, 07:04 PM (This post was last modified: 04-07-2015 07:25 PM by Gilles.)
Post: #3
 Gilles Member Posts: 171 Joined: Oct 2014
RE: HP50G Complex Number CAS manipulations
Quote:Let's suppose, we have the equation
z^2 − z = 0 and we want to solve for z, which is complex.

to solve this, I just do :

1/ Verify you are in complex mode (LShift & i to toggle mode if necessary)
2/ 'z^2 − z' 'z' SOLVE

For the ABS see flag 128 (variables are only real, or variables can be complex) (but it's unclear for me what does exactly this flag)
04-07-2015, 07:43 PM
Post: #4
 Hammonds Junior Member Posts: 3 Joined: Apr 2015
RE: HP50G Complex Number CAS manipulations
Yes, I'm in complex mode, but thanks for the shortcut.

I must be doing something stupid somewhere, as ABS still doesn't expand the expression, and when I do:

'z^2 − z' 'z' SOLVE

I just get:
{z=0 z=1}

I changed flag 128, but no difference.

I'm asking this because in that document, the author goes on to list a program that allows numerical solving on complex variables - which sounds very interesting, but it hinges on substituting parts of the expression that is expanded by ABS.

Thanks
04-07-2015, 08:07 PM (This post was last modified: 04-07-2015 08:19 PM by Gilles.)
Post: #5
 Gilles Member Posts: 171 Joined: Oct 2014
RE: HP50G Complex Number CAS manipulations
(04-07-2015 07:43 PM)Hammonds Wrote:  I must be doing something stupid somewhere, as ABS still doesn't expand the expression, and when I do:

'z^2 − z' 'z' SOLVE

I just get:
{z=0 z=1}

It's the correct answer (for example 'z²=-1' 'z' SOLVE returns {z=-i , z=i }

Quote:I changed flag 128, but no difference.

Uncheck flag 128 (Cmplx var allowed)
Complex mode

Then do

'z^2-z=0' ABS

and you get the result with RE and IM parts....
Code:
'SQRT(RE(z)^4+(2*IM(z)^2+2)*RE(z)^2+(IM(z)^4-2*IM(z)^2+1))=0'
04-07-2015, 08:23 PM
Post: #6
 Hammonds Junior Member Posts: 3 Joined: Apr 2015
RE: HP50G Complex Number CAS manipulations
It is working now.

Thank you.
 « Next Oldest | Next Newest »

User(s) browsing this thread: 1 Guest(s)