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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.

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.

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)

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 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....

It is working now.

Thank you.