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HP50G Complex Number CAS manipulations - Hammonds - 04-07-2015 06:24 PM
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.
RE: HP50G Complex Number CAS manipulations - Gerald H - 04-07-2015 07:03 PM
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.
RE: HP50G Complex Number CAS manipulations - Gilles - 04-07-2015 07:04 PM
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)
RE: HP50G Complex Number CAS manipulations - Hammonds - 04-07-2015 07:43 PM
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
RE: HP50G Complex Number CAS manipulations - Gilles - 04-07-2015 08:07 PM
(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'RE: HP50G Complex Number CAS manipulations - Hammonds - 04-07-2015 08:23 PM
It is working now.
Thank you.