HP 50g, degree mode, complex polar numbers w/ negative angle

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HP Forum Archive 18

HP 50g, degree mode, complex polar numbers w/ negative angle
Message #1 Posted by Paul Ozog on 20 Oct 2008, 11:30 p.m.

If I try to get the (Re, Im) format of:
exp(-22.6*i)
I get (-.843, .539). Isn't this blatantly wrong? Just think about it. The Re coordinate must be positive, and the Im negative. Note the calc is in degree mode. Am I missing something? This is pissing me off to no avail.


Re: HP 50g, degree mode, complex polar numbers w/ negative angle
Message #2 Posted by Karl Schneider on 21 Oct 2008, 1:46 a.m.,
in response to message #1 by Paul Ozog

Quote:
If I try to get the (Re, Im) format of:
exp(-22.6*i)
I get (-.843, .539). Isn't this blatantly wrong?
Paul --
It's wrong, alright.

Quote:
Just think about it. The Re coordinate must be positive, and the Im negative. Note the calc is in degree mode. Am I missing something?
Hmm, polar and degree mode. Maybe you meant,
1.00 / -22.6 degrees?
That converts to 0.92321 - i*0.38430 in rectangular mode.
However, you specified a complex number in rectangular form. I cannot obtain your result for antilogarithm. I don't have an HP-50g, but I do have practically every other HP calculator with built-in complex-number support. Every one I've tried yields the same answer, in degree or radians mode:
e^(-i*22.6) ~= -0.82031 + i*0.57193
I even evaluated your expression as an algebraic expression on the HP-49g and HP-48G, and got the same answer.
By Euler's Theorem,
e^ix = (cos x) + i*(sin x) [x in radians]
Degrees mode will be ignored by the HP models for complex-number calculations, because exponential (natural antilogarithm) requires a physically dimensionless input.
-- KS

Edited: 21 Oct 2008, 1:59 a.m.

Re: HP 50g, degree mode, complex polar numbers w/ negative angle
Message #3 Posted by V-PN on 21 Oct 2008, 2:19 a.m.,
in response to message #2 by Karl Schneider

My 50g functions correctly check your input, please The explanation given by Karl is correct

Re: HP 50g, degree mode, complex polar numbers w/ negative angle
Message #4 Posted by Marcus von Cube, Germany on 21 Oct 2008, 2:31 a.m.,
in response to message #2 by Karl Schneider

On a TI (Voyage 200) you can simply type e^(-22.6°*i) and get the intended result.
On the HP however, EXP(-22.6_°*i) cannot be evaluated; it's displayed as
e^{-(22.6*1_°*i)}
but EVAL or ->NUM fail with the message "Bad Argument Type". You can use the D->R function instead:
EXP(D->R(-22.6)*i)
works as intended and returns (0.9232,-0.3843) if you press ->NUM.

Re: HP 50g, degree mode, complex polar numbers w/ negative angle
Message #5 Posted by Paul Ozog on 21 Oct 2008, 7:48 p.m.,
in response to message #4 by Marcus von Cube, Germany

Whoops - forgot that (strictly speaking) Euler takes the angle to be in radians. You can't blame me when I'm surrounded by people typing exp(-22.6*i) in ti calcs, and when my electromagnetics textbook always gives polar-form complex numbers in degrees. Thanks for the help.

Re: HP 50g, degree mode, complex polar numbers w/ negative angle
Message #6 Posted by V-PN on 22 Oct 2008, 2:05 a.m.,
in response to message #4 by Marcus von Cube, Germany

This was actually the post that let me to understand the problem at hand - and to give the solution as well :-)

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