### Table of Contents

# DM41X 41z Module

## Keyboard Overlay

## Setup

- assign the
*complex keyboard*`Z`to USER menu on key`Σ+``SHIFT``ASN``ALPHA``Z``K``B``R``D``ALPHA``Σ+`- Enter
`USER`

mode with`USR`key - The
`Σ+`now activates a*complex number*function when it's pressed - for one operation only

### ZK?YN (UPDATE 5/8/22)

To simplify use it's possible change the keyboard to the *complex keyboard*, and remove the need to trigger *every* command with `Z`

Enable the keyboard with `ZK?YN`

and answer `Y`

.

Put `ZK?YN`

on the `CST`

custom user menu for quick access!

Now the `USER`

keyboard is re-mapped to match the overlay and things are much easier. To use `normal`

functions simply press `USR` to temporarily switch off the *complex keyboard*. Press `USR` to switch back to *complex* mode. To leave *complex* mode completely and return `USER`

keyboard to normal re-run `ZK?YN`

and answer `N`

To enter a complex number in this mode :

`2 + 3i`

`2` `ENTER` `3` `ENTER`

To add `2 + 3i`

`+`

`10 - 4i`

`2` `ENTER` `3` `ENTER`

`10` `ENTER` `4` `CHS` `ENTER`

`+`

Result:

`12 - j 1`

The alternative “permanent Z-Keyboard” method is less cumbersome and more intuitive.

#### Some commands still require the Z prefix to access sub-functions

e.g. `POLAR`

mode

Enter a complex number in rectangular mode and then switch to `POLAR`

mode

`50` `ENTER` `23` `ENTER`

`Z``Z``6`

`55.04 ∠ 24.70`

All further entries will remain as `POLAR`

eg a new complex number in POLAR format

`100 ∠ - 85`

`100` `ENTER` `85``CHS` `ENTER`

display :

`100 ∠ - 85`

Switch back to `RECT`

mode

`Z``Z``5`

`8.72 - 99.62`

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

## 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`

## 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`

### 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`

#### Z-keys method

`50` `ENTER` `13` `ENTER`

`1/x`

`23` `ENTER` `85``CHS` `ENTER`

`1/x`

`+`

`1/x`

Result :

`42.72 - j 11.99`

### convert to Rectangular ⇔ Polar operation

`Z = 50 - j 23`

- in polar form…
- enter Z as usual
- 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`

### Alternate input method

- 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: 05/09/24 11:38 BST