**HP 42S/DM 42/Free42: Argument, Real Part, Imaginary Part, and Sign Function**

**Introduction**

The HP 42S* has only one extraction function for complex numbers: ABS (absolute value) by default. To complete the list, here are some programs for ARG (argument), REAL (real part), and IMAG (imaginary part). The three functions take a complex number, in either rectangular or polar form.

Using stack commands and flag checks, I am able to get obtain results without affecting the stack much (although the z and t stacks will have the same value).

Also included is the SIGN (signum) function.

* This applies to the Swiss Micros DM42 (it should work), Free42 from Thomas Oakken, and any other HP 42S emulator apps. The print out is from Free42 (and I also have a physical HP 42S).

**HP 42S Program: ARG**

00 { 19-Byte Prgm }

01▸LBL "ARG"

02 COMPLEX

03 X<>Y

04 FC? 73

05 →POL

06 R↑

07 STO ST Y

08 R↓

09 R↓

10 RTN

11 .END.

**HP 42S Program: REAL**

00 { 21-Byte Prgm }

01▸LBL "REAL"

02 COMPLEX

03 X<>Y

04 FS? 73

05 →REC

06 X<>Y

07 R↑

08 STO ST Y

09 R↓

10 R↓

11 RTN

12 END

**HP 42S Program: IMAG**

00 { 20-Byte Prgm }

01▸LBL "IMAG"

02 COMPLEX

03 X<>Y

04 FS? 73

05 →REC

06 R↑

07 STO ST Y

08 R↓

09 R↓

10 RTN

11 END

Example - Rectangular Mode:

7+8i (7 [ENTER] 8 [ (shift) ] (COMPLEX) )

XEQ ARG: 48.8141 (Degrees)

XEQ REAL: 7.0000

XEQ IMAG: 8.0000

Example - Polar Mode: (Degrees):

4 ∡ 60 (4 [ENTER] 60 [ (shift) ] (COMPLEX) )

XEQ ARG: 60.0000

XEQ REAL: 2.0000

XEQ IMAG: 3.4641

**HP 42S Program: SIGN**

00 { 15-Byte Prgm }

01▸LBL "SIGN"

02 X=0?

03 RTN

04 ENTER

05 ABS

06 X<>Y

07 ÷

08 RTN

09 END

Example:

-1.4641 XEQ SIGN returns -1

5.525 XEQ SIGN returns 1

0 XEQ SIGN returns 0

Eddie

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