Complex Number Multi-Tool

The Complex Number Multi-Tool is a program for the HP 35S calculator which combines a few missing functions into one label.

Features

1. Convert rectangular to polar coordinates.
2. Convert polar to rectangular coordinates.
3. Get the real value.
4. Get the imaginary value.
5. Get the complex conjugate.

Usage

Run the program with with XEQ, I, and ENTER. The menu will flash three messages with numbers one to five for the five tools. Enter your selection at the prompt.

Requirements

1. Convert rectangular to polar coordinates:
   Input: A complex number stored in the X register.
   Output: x theta y, where the x-value is stored in the X register, and the y-value is stored in the Y register.
2. Convert polar to rectangular coordinates:
   Input: x theta y, where the x-value is stored in the X register, and the y-value is stored in the Y register.
   Output: A complex number stored in the X register.
3. Get the real value:
   Input: A complex number stored in the X register.
   Output: The real value stored in the X register.
4. Get the imaginary value:
   Input: A complex number stored in the X register.
   Output: The imaginary value stored in the X register.
5. Get the complex conjugate:
   Input: A complex number stored in the X register.
   Output: The complex conjugate stored in the X register.

Program Instructions

I001    LBL I
I002    SF 10                                   // Set Flag 10 to use EQN as text for menu
I003    EQN 1=POLAR 2=RECT
I004    PSE
I005    EQN 3=REAL  4=IMAG
I006    PSE
I007    EQN 5=COMPLEX CONJ
I008    PSE
I009    CF 10                                   // Return EQN to normal mode
I010    INPUT S                                 // Prompt for user selection
I011    1
I012    X=Y?                                    // Test if selection is Convert to Polar
I013    GTO I031
I014    Roll down                               // Enter the "Roll down" key
I015    2
I016    X=Y?                                    // Test if selection is Convert to Rectangular
I017    GTO I038
I018    Roll down
I019    3
I020    X=Y?                                    // Test if selection is Get Real Value
I021    GTO I045
I022    Roll down
I023    4
I024    X=Y?                                    // Test if selection is Get Imaginary Value
I025    GTO I054
I026    RCL C
I027    5
I028    X=Y?                                    // Test if selection is Complex Conjugate
I029    GTO I063
I030    RTN                                     // Exit program if no suitable user choice entered
I031    Roll down                               // Start of Convert to Polar routine
I032    Roll down
I033    ENTER
I034    ARG
I035    LASTx
I036    ABS
I037    RTN                                     // End of Convert to Polar routine
I038    EQN [REGZ*SIN(REGT),REGZ*COS(REGT)]     // Start of Convert to Rectangular routine
I039    [1,0]
I040    x<>y
I041    *
I042    EQN LASTx*[0,1]
I043    EQN REGX+i*REGY                         // Enter "REGX" as four variables, R, E, G, X.
I044    RTN                                     // End of Convert to Rectangular routine
I045    Roll down                               // Start of Get Real Value routine
I046    Roll down
I047    ENTER
I048    ARG
I049    COS
I050    x<>y
I051    ABS
I052    *
I053    RTN                                     // End of Get Real Value routine
I054    Roll down                               // Start of Get Imaginary Value routine
I055    Roll down
I056    ENTER
I057    ARG
I058    SIN
I059    x<>y
I060    ABS
I061    *
I062    RTN                                     // Start of Get Imaginary Value routine
I063    Roll down                               // Start of Complex Conjugate routine
I064    Roll down
I065    ENTER
I066    ABS
I067    x^2                                     // Enter the "X squared" key
I068    x<>y
I069    /
I070    RTN                                     // End of Complex Conjugate routine

Resources Used

The following programs served as references:

• Paul Dale's polar and rectangular conversions.
• Antonio Maschio's complex number decomposition.
• Karl Schneider's complex conjugate conversion.
• PickyBart's single label curve fitting program for the menu system.
• Stefan Vorkoetter's Matrix Multi-Tool for the name and the idea to consolidate the tools.