Complex Numbers in BASIC

[user5923]

I need to use complex number in number in BASIC, but
i = sqr(-1)
returns the following error:

Runtime Error: Float invalid operation

I don't know if there is a library or a separate command to use for this.

I looked for documentation on this, but couldn't find any.

Thanks for any help!

[tenochtitlanuk]

Anatoly & I, among others, have written sets of complex operators. Complex numbers don't exist in LB so we pack the real and imaginary parts as a string with two part s, and write routines to display and manipulate them with all the usual operations.
You could look at my pages at
www.diga.me.uk/complexity.html
www.diga.me.uk/NRcomplexRoots.html
I think tsh73 ( Anatoly) pit his routines up- was it on the #Programmer's Encyclopedia.

[user5923]

Apr 11, 2023 13:30:54 GMT -5 tenochtitlanuk said:

Anatoly & I, among others, have written sets of complex operators. Complex numbers don't exist in LB so we pack the real and imaginary parts as a string with two part sand write routines to display and manipulate them with all the usual operations.
You could look at my pages at
www.diga.me.uk/complexity.html
www.diga.me.uk/NRcomplexRoots.html
I think tsh73 ( Anatoly) pit his routines up- was it on the #Programmer's Encyclopedia.

Thanks for the response! I'm a beginner BASIC user, is there a specific way for me to implement this in my project? I need to be able to use and manipulate complex numbers.

[tsh73]

Hello
My version of complex library got dusted off recently (Jan 2023) in this thread
justbasiccom.proboards.com/thread/952/random-picture
probably six-th post, with three pictures and long code.

BUT

---

only things it has is
function compl$(Re, Im) 'make a complex of two reals Re Im
'breaking it back apart
function Re(compl$)
function Im(compl$)
'some formatting
function formatCompl$(compl$) 'tried to zero things like 1e-15, but this is just for display anyway
'+ _ * /
function addCompl$(c1$, c2$)
function subCompl$(c1$, c2$)
function mulCompl$(c1$, c2$)
function divCompl$(c1$, c2$)
'Conjugation
function barCompl$(c1$)
'abs (polar radius)
function absCompl$(c1$)
'And you can get polar angle as
atan2(Im(r$), Re(r$)

The point is, there are no SQRT unction.
BUT... since we can translate number to (r, phi) polar from
we could use
en.wikipedia.org/wiki/De_Moivre%27s_formula

Just tried to add this below:
function RPhi2compl$(r, phi) '(r, phi) -> Re+i*Im
function powerCompl$(c1$,n) 'n supposed to be integer
function rootCompl$(c1$,n) 'n supposed to be integer
'and i-th root
'not really sure about phi, but it works for real numbers
function rootICompl$(c1$,n,i) 'n supposed to be integer, is supposed to be 1..n

---

So part below
'-------------------------------------
'complex library.

is a library (set of functions)
Just put it into your program and go ahead.

Complex number is stored as a space-delimited string of "re_part im_part"
(so "0 0" is a valid 0)

and since we cannot overload operators in LB - we have to use functions for all operators
And nest them properly/ And close all the brackets (!).
it tends to be rather weird looking, like this

   f$ = subCompl$("0 0" , addCompl$("1 0", addCompl$(z$, mulCompl$(z$, mulCompl$(z$, z$)))))
instead of
f= 0-(1+z+z*z*z)
)

(There was a library for interface existing in C++ and Pascal. (actually Borland's TurboVision)
And in C++, they just overloaded + operator and used it to add stuff.
While in Pascal they had to use just the same chain of functions like I here.
)

But still better then multiply (or god forbid divide) complex numbers by hand!

---

And
zz$=rootCompl$(compl$(1,0),2)
print formatCompl$(zz$)

is actually sqr(-1)

---

'complex library test
a$=compl$(1,0)
print formatCompl$(a$)
b$=compl$(0,1)
print formatCompl$(b$)

print
z$ = mulCompl$(b$, b$)
print formatCompl$(z$)

print
zz$=rootCompl$(compl$(1,0),2)
print formatCompl$(zz$)
print formatCompl$( powerCompl$(zz$,2))

print
zz$=rootCompl$(compl$(0,1),2)
print formatCompl$(zz$)
print formatCompl$( powerCompl$(zz$,2))

print
print "5 roots of 1"
for i = 1 to 5
   zz$=rootICompl$(compl$(1,0),5,i)
   print formatCompl$(zz$) ,"-> ";  formatCompl$(powerCompl$(zz$,5))
next



end

'---------------------------
function atan2(y,x)
   pi = acs(-1)    'could be made global to save some ticks
   if x <> 0 then arctan = atn(y/x)

   select case
       case x > 0
       atan2 = arctan

       case y>=0 and x<0
       atan2 = pi + arctan

       case y<0 and x<0
       atan2 = arctan - pi

       case y>0 and x=0
       atan2 = pi / 2

       case y<0 and x=0
       atan2 = pi / -2
   end select
end function

'-------------------------------------
'+ powers and roots

'first, r and phi as numbers
function angleCompl$(c1$)
   angleCompl = atan2(Im(c1$), Re(c1$) )
end function

function absCompl(c1$)
   Re=Re(c1$)
   Im=Im(c1$)
   absCompl = sqr(Re*Re+Im*Im)
end function

'and back
function RPhi2compl$(r, phi)  'you better inline this, actually
   RPhi2compl$= str$(r*cos(phi))+" "+ str$(r*sin(phi))
end function


'then power
function powerCompl$(c1$,n) 'n supposed to be integer
   Re=Re(c1$)
   Im=Im(c1$)
   r=sqr(Re*Re+Im*Im)
   phi=atan2(Im, Re)
   powerCompl$ = RPhi2compl$(r^n, phi*n)
end function

function rootCompl$(c1$,n) 'n supposed to be integer
   Re=Re(c1$)
   Im=Im(c1$)
   r=sqr(Re*Re+Im*Im)
   phi=atan2(Im, Re)
   if phi = 0 then phi = 2*acs(-1) '2*pi
    rootCompl$=RPhi2compl$(r^(1/n), phi/n)
end function

'and i-th root
'not really sure about phi
function rootICompl$(c1$,n,i) 'n supposed to be integer, is supposed to be 1..n
   Re=Re(c1$)
   Im=Im(c1$)
   r=sqr(Re*Re+Im*Im)
   phi=atan2(Im, Re)
   if phi = 0 then rhi = 2*acs(-1) '2*pi
    rootICompl$=RPhi2compl$(r^(1/n), phi/n+(i-1)*2*acs(-1)/n)
end function

'-------------------------------------
'complex library. I jsut was too lazy to multiply complex numbers by hand.
function absCompl$(c1$)
   Re=Re(c1$)
   Im=Im(c1$)
   abs=sqr(Re*Re+Im*Im)
   absCompl$ = str$(abs)
end function

'Conjugation
function barCompl$(c1$)
   Re=Re(c1$)
   Im=0-Im(c1$)
   barCompl$ = str$(Re)+" "+ str$(Im)
end function

function divCompl$(c1$, c2$)
'(a + bi)/(c + di): = (ac + bd)/(c^2+d^2) + (bc - ad)/(c^2+d^2)i.
   a=Re(c1$)
   b=Im(c1$)
   c=Re(c2$)
   d=Im(c2$)
   dd=c*c+d*d
   divCompl$ = str$((a*c + b*d)/dd) +" " + str$((b*c - a*d)/dd)
end function

function mulCompl$(c1$, c2$)
'(a + bi)(c + di): = (ac - bd) + (bc + ad)i.
   a=Re(c1$)
   b=Im(c1$)
   c=Re(c2$)
   d=Im(c2$)
   mulCompl$ = str$(a*c - b*d) +" " + str$(b*c + a*d)
end function

function subCompl$(c1$, c2$)
   Re=Re(c1$)-Re(c2$)
   Im=Im(c1$)-Im(c2$)
   subCompl$ = str$(Re)+" "+ str$(Im)
end function

function addCompl$(c1$, c2$)
   Re=Re(c1$)+Re(c2$)
   Im=Im(c1$)+Im(c2$)
   addCompl$ = str$(Re)+" "+ str$(Im)
end function

function formatCompl$(compl$)
   Re = Re(compl$)
   Im = Im(compl$)
   'approx: clear "near zero" parts.
   'This is just visualizing!
       if abs(Re)<1e-10 then Re=0
       if abs(Im)<1e-10 then Im=0
   if Re=0 and Im=0 then  formatCompl$ = "0": exit function
   Re$ = word$(compl$,1)
   if Re =0 then Re$=""    'and no next "+"
   Im$=str$(Im)+"i"
   if Im =0 then Im$=""
   formatCompl$ = Re$+ iif$(Im>0 and Re<>0, "+", "")+ Im$
end function

function Re(compl$)
   Re = val(word$(compl$,1))
end function

function Im(compl$)
   Im = val(word$(compl$,2))
end function

function compl$(Re, Im)  'you better inline this, actually
   compl$= str$(Re)+" "+ str$(Im)
end function

'-----------------------------------
function iif(test, valYes, valNo)
   iif =  valNo
   if test then iif =  valYes
end function

function iif$(test, valYes$, valNo$)
   iif$ =  valNo$
   if test then iif$ =  valYes$
end function