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From: Heiko on 11 Mar 2010 12:54
Moin Moin!

I recently bought myself a HP 49 G and I am still learning how to use
it
effectively.

I am able to do most of my tasks with it but there are still some
bumps
on the road...

Maybe you could help me with this...I think it is a real newbie
question...

I want to "solve" this xroot:

xroot ( 4, 4+i )

What do I have to do to make the HP calculate the four roots??

Any help would be wonderful!

Thanks a lot!

Best, Heiko
From: Han on 11 Mar 2010 14:54
On Mar 11, 12:54 pm, Heiko <cico0...(a)gmx.de> wrote:
> Moin Moin!
>
> I recently bought myself a HP 49 G and I am still learning how to use
> it
> effectively.
>
> I am able to do most of my tasks with it but there are still some
> bumps
> on the road...
>
> Maybe you could help me with this...I think it is a real newbie
> question...
>
> I want to "solve" this xroot:
>
> xroot ( 4, 4+i )
>
> What do I have to do to make the HP calculate the four roots??
>
> Any help would be wonderful!
>
> Thanks a lot!
>
> Best, Heiko

There are several ways to represent a complex number. You may want to
consider the form (a,b) where (a,b) = a+bi. Then just take the square
root of (a,b) twice. This gives you one of the four roots (the
principal root). Just take appropriate powers of the principal root to
find the other ones.

Don't forget you can also convert a+bi to exponential form: a+bi =
r*e^{i*t} where r = sqrt(a^2+b^2) and t = arctan(b/a). Then taking the
fourth root can be done via raising to the fractional power 1/4.

(a+bi)^{1/4} = r^{1/4} e^{i*t/4}

Han
From: supergems on 11 Mar 2010 15:09
On 11 Mar, 18:54, Heiko <cico0...(a)gmx.de> wrote:
> Moin Moin!
>
> I recently bought myself a HP 49 G and I am still learning how to use
> it
> effectively.
>
> I am able to do most of my tasks with it but there are still some
> bumps
> on the road...
>
> Maybe you could help me with this...I think it is a real newbie
> question...
>
> I want to "solve" this xroot:
>
> xroot ( 4, 4+i )
>
> What do I have to do to make the HP calculate the four roots??
>
> Any help would be wonderful!
>
> Thanks a lot!
>
> Best, Heiko

In RPN mode:

\<< OVER ABS OVER XROOT UNROT SWAP
ARG 0 PICK3 1 -
FOR j 2 \pi * j * OVER + i *
PICK3 / EXP 4 PICK * 4 ROLLD
NEXT DROP NIP \->LIST EXPAND
\>> 'CPROOTS' STO

syntax: X N CPROOTS, where X is a complex or real number and N is the
integer degree of the root.
CPROOTS uses de Moivre's formula.

'4+i' 4 CPROOTS --> { 'XROOT(4,\v/17)*EXP(i*ATAN(1/4)/
4)' 'XROOT(4,\v/17)*EXP((i*ATAN(1/
4)+2*i*\pi)/4)' 'XROOT(4,\v/17)*EXP(
(i*ATAN(1/4)+4*i*\pi)/4)' 'XROOT(4
,\v/17)*EXP((i*ATAN(1/4)+6*i*\pi)/4)
' }

XNUM -->

{
(1.42229965901,8.72173426437E-2)
(-8.72173426484E-2,1.42229965901)
(-1.42229965901,-8.72173426557E-2)
(8.72173426202E-2,-1.42229965901)
}

another example:

-8 3 CPROOTS --> { '1+i*\v/3' -2 '1-i*\v/3' }
From: Heiko on 12 Mar 2010 01:30
On 11 Mrz., 21:09, supergems <simone.cer...(a)gmail.com> wrote:
> On 11 Mar, 18:54, Heiko <cico0...(a)gmx.de> wrote:

[..] snipp

> -8 3 CPROOTS --> { '1+i*\v/3' -2 '1-i*\v/3' }

Great!!! Thank you so much!!

Best, Heiko
From: John H Meyers on 12 Mar 2010 04:28
On 3/11/2010 11:54 AM, Heiko wrote:

> I want to "solve" this xroot:
> xroot ( 4, 4+i )
> What do I have to do to make the HP calculate the four roots??

I seem to recall that XROOT is confined to real-valued inputs and outputs,
having been invented specifically to avoid complex-valued results in,
for example 'XROOT(3,-8.)'

On the other hand, [ -1. 0 0 0 (4,1) ] PROOT solves '-X^4+(4,1)=0'
giving the four answers immediately, on all HP48G/49G/50G, thus:

@ All n'th roots of x (HP48G/49G/50G)
@ (where n is an integer > 0 and x is numeric)
\<< \-> n x \<< -1. 1. n START 0. NEXT DROP
x 'n' INCR \->ARRY PROOT \>> \>> 'xroot' STO

Example: 'xroot(4,(4,1))' EVAL

[r->] [OFF]
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