# partial fractions and complex roots in 50g - Hewlett Packard

This is a discussion on partial fractions and complex roots in 50g - Hewlett Packard ; Hello, Doing partial fractions with this in the denominator: s^2+10s+169 gives me a crazy result. When I simply factor this, I know why. I get something involving e^i*ATAN(12/5) etc. All I really want is (s+5-12i) (s+5+12j). I played with most ...

# Thread: partial fractions and complex roots in 50g

1. ## partial fractions and complex roots in 50g

Hello,

Doing partial fractions with this in the denominator: s^2+10s+169
gives me a crazy result. When I simply factor this, I know why. I get
something involving e^i*ATAN(12/5) etc. All I really want is (s+5-12i)
(s+5+12j).
I played with most of the simplification functions in the ALG and
EXP&LN menus, but none really makes a difference.
I know it's not too hard to do by hand, but that's not why I have this
calculator.

Ultimately I want to get the partial fractions with an expression like
that in the denominator, which I then take the inverse Laplace
transform of. It works great with real roots, just not with complex
roots.

Any ideas?

Thanks!

Christoph

2. ## Re: partial fractions and complex roots in 50g

On 16 Okt., 17:46, Christoph Koehler
wrote:

> Doing partial fractions with this in the denominator: s^2+10s+169
> gives me a crazy result. When I simply factor this, I know why.

On my 50g it works like this
Choose MODE CAS and check the flag for Complex, OK

Then type enter x^2+10*x+169 and choose EDIT and FACTO
and you get the result, you want

Regards,
Peter

3. ## Re: partial fractions and complex roots in 50g

If you try it with RECT (rectangular coordinates) mode and Complex
mode both turned on, I think it will do what you want. Having the
coordinates in Polar or Spherical modes causes some complex
expressions to be displayed in polar form, r*exp(i*theta), instead of
rectangular form, a+bi. I've noticed this mode setting also affects
certain integrals.

-wes

On Oct 16, 6:46*pm, Christoph Koehler
wrote:
> Hello,
>
> Doing partial fractions with this in the denominator: s^2+10s+169
> gives me a crazy result. When I simply factor this, I know why. I get
> something involving e^i*ATAN(12/5) etc. All I really want is (s+5-12i)
> (s+5+12j).
> I played with most of the simplification functions in the ALG and
> EXP&LN menus, but none really makes a difference.
> I know it's not too hard to do by hand, but that's not why I have this
> calculator.
>
> Ultimately I want to get the partial fractions with an expression like
> that in the denominator, which I then take the inverse Laplace
> transform of. It works great with real roots, just not with complex
> roots.
>
> Any ideas?
>
> Thanks!
>
> Christoph

4. ## Re: partial fractions and complex roots in 50g

On Oct 16, 12:10*pm, Wes wrote:
> If you try it with RECT (rectangular coordinates) mode and Complex
> mode both turned on, I think it will do what you want. *Having the
> coordinates in Polar or Spherical modes causes some complex
> expressions to be displayed in polar form, r*exp(i*theta), instead of
> rectangular form, a+bi. *I've noticed this mode setting also affects
> certain integrals.

I am so glad you figured that out. That was exactly it, and it makes a
lot of sense.

Thanks again!

Christoph

5. ## Re: partial fractions and complex roots in 50g

On Thu, 16 Oct 2008 10:10:43 -0700 (PDT), Wes
wrote:

>If you try it with RECT (rectangular coordinates) mode and Complex
>mode both turned on, I think it will do what you want. Having the
>coordinates in Polar or Spherical modes causes some complex
>expressions to be displayed in polar form, r*exp(i*theta), instead of
>rectangular form, a+bi. I've noticed this mode setting also affects
>certain integrals.
>

Could you please point me to ANY HP50 manual where the above procedure
is described?

A.L.

6. ## Re: partial fractions and complex roots in 50g

No problems on the 50g turn the calculator on clear all entries enter equation in frequency domain then white left arrow key then (1) and selection 2 Polynomial and then 15 Partfrac and then if you just want to find the inverse laplace follow below.

clear all entries on screen go into CALC menu by pressing white left arrow then key (4) select 3 Differential equations then 2 ILAP and enter the equation in the frequency domain f(s) to get f(t) as the answer. To do it manually eg to find the inverse laplace 1/(s^2+s+1) it needs the form As+B/(s^2+s+1). Then
1/(s^2+s+1)=As+B/(s^2+s+1) therefore 1=As+B when A=0; B=1

(0(s+0.5)/(s+0.5)^2+0.75)+(1/(s+0.5)^2+0.75) the denominators in perfect squares
From the inverse laplace transform tables you may derive that the solution is

(0e^(-0.5t))*cos(((0.75)^0.5)t)+(1/(0.75)^0.5)(e^(-0.5t))*sin(((0.75)^0.5)t)

I believe this to be correct