DM41X 41z Module

Keyboard Overlay

Setup

assign the complex keyboard Z i.e. function ΣZL to USER menu on key Σ+
- SHIFT ASN ALPHA SHIFT F Z L ALPHA Σ+
  - SHIFT F is the method of getting Σ from the ALPHA keyboard (see the back of calculator)
- Enter USER mode with USR key
- The Σ+ now activates a complex number function when it's pressed - for one operation only

The rest of the guide was written without the use of full-time ZKEYS in mind

in the forum thread dealing with the factorization bug in the deluxe version Angel recommended I use the ΣZL method. He fears that occasionally ZKEYS might be broken with incorrect/missing USER assignments - so I'll try to stick to the normal ΣZL method.

Quick Ref

Z = Σ+

↑IM/AG = Z XEQ
ZREAL↑ = Z Z RCL
ZIMAG↑ = Z Z XEQ
ZINV = Z 1/X
POLAR = Z Z R→P (i.e. 6)
RECT = Z Z P→R (i.e. 5)
ZCONJ = Z SHIFT CHS (complex conjugate)
Z ^ X = Z EEX
Z ^ 1/X = Z Z EEX (root(s) of complex number) : see Cubic Roots
- ZNXTNRT _ = Z Z SHIFT √x NEXT ROOT enter the root you want
ZWDOT = ZZ. : dot product of 2 vectors/complex numbers
ZWCROSS = ZZ2 : Magnitude of the Cross Product of 2 vectors/complex numbers (no sign)
ZWDET = ZZ7 : Determinant (Cross Product) of 2 vectors/complex numbers, incl. sign/direction

Basic Operation

enter two numbers and add them together

The ''natural'' entry method

Enter a complex number to the stack
- 5 + j 20
  - 5 Z XEQ 2 0 ENTER
    - Z XEQ is ^IM/AG - set the imaginary part
add a second number to the stack
- 10 - j 32
  - 10 Z XEQ 3 2 CHS ENTER
add the two numbers together
- Z +
15 - j 12

Enter a real number

2.75 + j 0
- 2.75 Z Z RCL

Enter an imaginary number

0 + j 3.1415 (i Pi)
- SHIFT π Z Z XEQ

Use it to calculate with....

calculate e^iπ
- Z SHIFT e^x
- - 1 + j 0
- e^iπ = -1

Parallel Impedances

This involves the complex inverse function Z 1/x

Z1 = 50 + j 13 in parallel with Z2 = 23 - j 85
- enter Z1 50 Z XEQ 13 ENTER and invert it Z 1/X
  - 0.02 - j 4.87E-3
- enter Z2 23 Z XEQ 85 CHS ENTER and invert it Z 1/X
  - 2.97E-3 + j0.01
- add them together Z +
  - 0.02 +j0.01 and invert Z 1/X
    - 42.72 - j 11.99

convert to Rectangular ⇔ Polar operation

Z = 50 - j 23
initially in rectangular form…¹⁾
- enter Z as usual
  - 50 Z XEQ 23CHS ENTER
- convert to Polar format
  - Z Z 6 ( 6 is R→P but needs two presses of Z to activate it)
  - 55.04 ∠ -24.70
- convert back to Rectangular operation
  - Z Z 5
  - 50 - j 23

enter a number directly in Polar format

To enter 5 ∠ 53.13 directly
- switch to Polar format Z Z 6
- enter Mag / Angle:
  - 5 Z XEQ 53.13 ENTER
  - display : 5 ∠ 53.13
convert to Rect
- Z Z 5
  - display : 3.00 + j 4.00

Cubic Roots

Rectangular

enter complex real number -8 + j 0
- 8 CHS Z Z RCL
  - -8 + j 0
- enter 3 (goes into the normal X register)
- find the result of Z↑1/x
  - ZZEEX
    - 1 + j 1.732 (the first of the cube-roots of -8)
- find the next root with the function ZNXTNRT
  - ZZSHIFT√x
  - enter 3 at the _ prompt
    - -2 + j 0
- find the next root with the function ZNXTNRT
  - ZZSHIFT√x
  - enter 3 at the _ prompt
    - 1 - j 1.732

The 3 cube roots of -8 are

1 + j 1.732
-2 + j 0 (the basic real cube root)
1 - j 1.732

Polar

enter complex real number -8 + j 0
- 8 CHS Z Z RCL
  - -8 + j 0
  - convert to POLAR
    - ZZ6
      - 8 ∠ 180
- enter 3 (goes into the normal X register)
- find the result of Z↑1/x
  - ZZEEX
    - 2 ∠ 60.000 (the first of the cube-roots of -8)
- find the next root with the function ZNXTNRT
  - ZZSHIFT√x
  - enter 3 at the _ prompt
    - 2 ∠ 180
- find the next root with the function ZNXTNRT
  - ZZSHIFT√x
  - enter 3 at the _ prompt
    - 2 ∠ -60.000

The 3 cube roots (in POLAR) of -8 are

2 ∠ 60.000
2 ∠ 180
2 ∠ -60.000

Alternate input method

BEWARE

key Imaginary part first & press normal ENTER
key real part (and no ENTER)
do complex enter (Z ENTER) or another complex function (e.g. Z +) (be careful with the stack lift or it gets confusing)
e.g. 52 + j 36
- 36 ENTER 52 Z ENTER
- 52 + j 36 is now in Stack
enter second number
e.g. 23 - j 15
- 15 CHS ENTER 23 (don't Z ENTER this…!!)
to add them together use Z + now (instead of Z ENTER)
result : 75 + j 21

gotcha

pressing Z ENTER after the second number (instead of the required complex function) will give you

Stack value	Stack
	U
52 + j 36	V
23 - j 15	W
23 - j 15	Z

doing a Z + now will add the second number to itself and the result will be 46 - j 30

This is normal RPN stack behaviour, but is confusing when you're building complex numbers.

use ↑IM/AG instead

The natural entry mode is much better

you enter the real and imaginary parts in the order you expect them
the stack operation is less obscure.
It just seems more intuitive.

Page created Wed May 25 15:14:29 2022 by John Pumford-Green

Page last updated: 06/03/25 06:49 GMT

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¹⁾

Z Z 5 to make sure!

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