The absence of rectangular to polar, polar to rectangular and related functions on the HP 35s has already been discussed at length, and I believe that various routines are due to soon be included in the software library. Rather than wait, I attempted to go through the various threads to see if I could pull out the best routines for each function. However, I found it a bit tricky to follow the threads and various routines that were presented. To try to get a handle on things, I went back to the basics of the problem and tried to work my way forward. The following likely rehashes a lot of the previous discussion, and I make no claims of originality. So, at the risk of beating a dead horse (and exposing a blatant lack of understanding of some point or another), from the beginning.....

As I see things, there are seven basic functions related to the entry, display and conversion of complex numbers that the 35s lacks. For the sake of the following discussion, “Complex” means a complex number residing in a single stack level on the 35s, “Real Rectangular” means a complex number represented in rectangular form as two real values in two stack levels, and “Real Polar” means a complex number represented in polar form as two real values in two stack levels. The seven missing functions are:

- Complex to Real Rectangular Form conversion - Decomposition of a complex number into its real and imaginary components, with those values placed in the stack x and stack y registers, respectively.

- Complex to Real Polar Form conversion - Decomposition of a complex number into the magnitude and angle of its polar form, with those values placed in the stack x and stack y registers, respectively.

- Real Rectangular Form to Complex conversion - Formation of a complex number in stack x from real and imaginary components initially in the stack x and stack y registers, respectively.

- Real Polar Form to Complex conversion - Formation of a complex number in stack x from a magnitude and angle initially in the stack x and stack y registers, respectively.

- Real Polar to Real Rectangular Conversion - Conversion of a polar representation of complex number in stack x (magnitude) and stack y (angle) to a rectangular representation in stack x (real) and stack y (imaginary).

- Real Rectangular to Real Polar Conversion - Conversion of a rectangular representation of complex number in stack x (real) and stack y (imaginary) to a polar representation in stack x (magnitude) and stack y (angle).

- Complex Conjugate - Conversion of a complex number in stack x to its complex conjugate in stack x.

Re :a value representing the real component of a complex numberWith the above said, I believe that the previously described seven functions should perform as follows:

Im :a value representing the imaginary component of a complex number

Mag :a value representing the magnitude of a complex number when

expressed in polar form

Ang :a value representing the angle of a complex number when

expressed in polar form

A, B, C :specific pre-existing values in the stack

Re i Im :a complex number held in a single stack level displayed in

rectangular form

Mag/Ang :a complex number held in a single stack level displayed in

polar form

-- :the most recent value in the Last x register, to be overwritten

1. Complex to Real RectangularHaving come this far, I went ahead and developed seven routines to accomplish the above functions. I used many ideas and techniques developed in the previous discussion, and I don’t know if I exactly replicated any of the routines presented previously. If so, due credit is given to the original developer. I decided to place them all under one label, rather than having different labels for each. (In earlier threads, I found the labelling a bit confusing. Does Label P convert to Polar, from Polar, convert a complex number to real polar form, etc.?) I chose Label Z, for a couple of reasons. I intend for the program to be always resident on the calculator. Since Z is the last label alphabetically, I can easily remember that it is unavailable for general programming. Also, the letter Z is used to represent complex impedance in electric power engineering, which is my primary application for these functions, so it seemed natural to use it for this suite of functions. Each routine has an equation at the beginning that labels the function to be performed. It is set up to pause, display the function name, then execute the routine when each routine is called. It is

Stack BeforeStack After

t: C -> t: B

z: B -> z: A

y: A -> y: Im

x: Re i Im or Mag/Ang -> x: Re

Last x: -- -> Last x: Re i Im or Mag/Ang2. Complex to Real Polar

Stack BeforeStack After

t: C -> t: B

z: B -> z: A

y: A -> y: Ang

x: Re i Im or Mag/Ang -> x: Mag

Last x: -- -> Last x: Re i Im or Mag/Ang3. Real Rectangular to Complex

Stack BeforeStack After

t: B -> t: B

z: A -> z: B

y: Im -> y: A

x: Re -> x: Re i Im or Mag/Ang

Last x: -- -> Last x: Re4. Real Polar to Complex

Stack BeforeStack After

t: B -> t: B

z: A -> z: B

y: Ang -> y: A

x: Mag -> x: Re i Im or Mag/Ang

Last x: -- -> Last x: Mag

5. Real Polar to Real Rectangular

Stack BeforeStack After

t: B -> t: B

z: A -> z: A

y: Ang -> y: Im

x: Mag -> x: Re

Last x: -- -> Last x: Mag6. Real Rectangular to Real Polar

Stack BeforeStack After

t: B -> t: B

z: A -> z: A

y: Im -> y: Ang

x: Re -> x: Mag

Last x: -- -> Last x: Re7. Complex Conjugate

Stack BeforeStack After

t: C -> t: C

z: B -> z: B

y: A -> y: A

x: Re i Im or Mag/Ang -> x: Re i -Im or Mag/-Ang

Last x: -- -> Last x: Re i Im or Mag/Ang

**not**independent of flag 10, which is set to display the function label, then cleared in each routine. So flag 10 will be cleared after each routine, regardless of its setting prior to execution. The routines use only stack manipulation and equations, no general storage registers are used. With the above caveats, my program to implement the suite of Complex-Rectangular-Polar functions is as follows:

Z001 LBL ZAnd, for what it’s worth,

Z002 SF 10 :Entry point for Complex to Rectangular

Z003 Eqn CPLX->RECT

Z004 PSE

Z005 CF 10

Z006 ABS

Z007 CLx

Z008 eqn ABS(LASTx)*SIN(ARG(LASTx))

Z009 eqn ABS(LASTx)*COS(ARG(LASTx))

Z010 RTN

Z011 SF 10 :Entry point for Complex to Polar

Z012 Eqn CPLX->POLAR

Z013 PSE

Z014 CF 10

Z015 ARG

Z016 LASTx

Z017 ABS

Z018 RTN

Z019 SF 10 :Entry point for Rectangular to Complex

Z020 Eqn RECT->CPLX

Z021 PSE

Z022 CF 10

Z023 ABS

Z024 Roll down

Z025 Roll down

Z026 Eqn LASTx+i*REGT

Z027 Eqn REGZ

Z028 Roll down

Z029 RTN

Z030 SF 10 :Entry point for Polar to Complex

Z031 Eqn POLAR->CPLX

Z032 PSE

Z033 CF 10

Z034 ABS

Z035 Roll Down

Z036 Roll Down

Z037 Eqn LASTx*COS(REGT)+i*LASTx*SIN(REGT)

Z038 Eqn REGZ

Z039 Roll Down

Z040 RTN

Z041 SF 10 :Entry point for Polar to Rectangular

Z042 Eqn POLAR->RECT

Z043 PSE

Z044 CF 10

Z045 ABS

Z046 Roll Down

Z047 Roll Down

Z048 Eqn LASTx*COS(REGT)+i*LASTx*SIN(REGT)

Z049 ENTER

Z050 Roll Down

Z051 Roll Down

Z052 Eqn ABS(REGZ)*SIN(ARG(REGZ))

Z053 Eqn ABS(REGT)*COS(ARG(REGT))

Z054 RTN

Z055 SF 10 :Entry point for Rectangular to Polar

Z056 Eqn RECT->POLAR

Z057 PSE

Z058 CF 10

Z059 ABS

Z060 CLx

Z061 LASTx

Z062 Roll Down

Z063 Roll Down

Z064 Eqn REGZ+i*REGT

Z065 ENTER

Z066 Roll Down

Z067 Roll Down

Z068 Eqn ARG(REGT)

Z069 Eqn ABS(REGT)

Z070 RTN

Z071 SF 10 :Entry point for Complex Conjugate

Z072 Eqn CPLX CONJUGATE

Z073 PSE

Z074 CF 10

Z075 ABS

Z076 CLx

Z077 Eqn SQ(ABS(LASTx))/LASTx

Z078 RTN

CK = F440

LN = 541