HP50G and solving equations with complex numbers

[Simone Cerica]

To solve systems of linear equations with complex coefficients you can use both LINSOLVE and SOLVE:

Code:

[ '(1+i)*X-Y=i' '(1-i)*X+(1+i)*Y=1' ] [ 'X' 'Y' ] LINSOLVE

returns

Code:

{ [ '(1+i)*X-Y=i' '(1-i)*X+(1+i)*Y=1' ] [ 'X' 'Y' ] }
:Specific: { '1+i' 1 1 1. }
[ 'X=(1+i)/2' 'Y=0' ]

to solve single equations numerically you can operate directly on the stack:



to enter complex numbers in polar form can be useful these programs:

Code:

\<< \-> X Y \<< { X Y } XNUM EVAL DEG -19. SF CYLIN \->V2 \>> \>> 'PN' STO

syntax: "module r" "argument φ" PN --> (r,\<)φ)
ex: '\v/2' 45 PN --> (1.41421356237,\<)45.)

Code:

\<< -16 FS? IF THEN -16 CF ELSE -16 SF END \>> 'RP' STO

RP switches from rectangular to polar notation and vice versa:
(1.,1.) RP --> (1.41421356237,\<)45.)
(1.41421356237,\<)45.) RP --> (1.,1.)

however, for more complex equations and non-linear systems for better use SolveSys as suggested by Han:

SolveSys 49 1.2
http://www.hpcalc.org/details/3145
SolveSys 49 Documentation
http://www.hpcalc.org/details/3146

Furthermore I strongly suggest you read the Complex Numbers Marathon: http://www.hpcalc.org/details/5114