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.

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. *

My 50g functions correctly

check your input, please

The explanation given by Karl is correct

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.

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.

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