DM41X 41z Module - Make It Tea

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====== DM41X 41z Module ======


===== Keyboard Overlay =====

{{ :public:calculator:guides:large_41z.png?400 |}}

===== Setup =====

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


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

++++ ZK?YN Info |

To simplify use it's possible change the keyboard to the //complex keyboard//, and remove the need to trigger //every// command with <key>Z</key>

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 <key>USR</key> to temporarily switch off the //complex keyboard//. Press <key>USR</key> 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''

<key>2</key> <key>ENTER</key> <key>3</key> <key>ENTER</key>

To add ''2 + 3i'' ''+'' ''10 - 4i''

<key>2</key> <key>ENTER</key> <key>3</key> <key>ENTER</key>

<key>10</key> <key>ENTER</key> <key>4</key> <key>CHS</key> <key>ENTER</key>

<key>+</key>

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

<key>50</key> <key>ENTER</key> <key>23</key> <key>ENTER</key>

<key>Z</key><key>Z</key><key>6</key>

''55.04 ∠ 24.70''

All further entries will remain as ''POLAR'' 

eg a new complex number in POLAR format 

''100 ∠ - 85''

<key>100</key> <key>ENTER</key> <key>85</key><key>CHS</key> <key>ENTER</key>

display : 

''100 ∠ - 85''


Switch back to ''RECT'' mode

<key>Z</key><key>Z</key><key>5</key>

''8.72 - 99.62''

++++

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

  * in the  [[https://forum.swissmicros.com/viewtopic.php?f=26&t=4029 | 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 =====

  * <key>Z</key> = <key>'Σ+'</key>

  * <key>↑IM/AG</key> = <key>Z</key> <key>XEQ</key>
  * <key>ZREAL↑</key> = <key>Z</key> <key>Z</key> <key>RCL</key>
  * <key>ZIMAG↑</key> = <key>Z</key> <key>Z</key> <key>XEQ</key>
  * <key>ZINV</key> = <key>Z</key> <key>1/X</key>
  * <key>POLAR</key> = <key>Z</key> <key>Z</key> <key>R→P</key> (i.e. <key>6</key>)  
  * <key>RECT</key> = <key>Z</key> <key>Z</key> <key>P→R</key>  (i.e. <key>5</key>)
  * <key>ZCONJ</key> = <key>Z</key> <key>SHIFT</key> <key>CHS</key> (complex conjugate)
  * <key>Z ^ X</key> = <key>Z</key> <key>EEX</key>
  * <key>Z ^ 1/X</key> = <key>Z</key> <key>Z</key> <key>EEX</key> (root(s) of complex number) : see [[#Cubic Roots of -8]]
    * <key>ZNXTNRT _</key> = <key>Z</key> <key>Z</key> <key>SHIFT</key> <key>'√x'</key> ''NEXT ROOT''  enter the root you want 
  
===== Basic Operation =====

==== enter two numbers and add them together ====

=== The ''natural'' entry method ===

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

==== Enter a real number ====

  * '' 2.75 + j 0 ''
    * <key>2.75</key> <key>Z</key> <key>Z</key> <key>RCL</key>

==== Enter an imaginary number ====

  * '' 0 + j 3.1415 '' (i Pi)
    * <key>SHIFT</key> <key>π</key> <key>Z</key> <key>Z</key> <key>XEQ</key>

=== Use it to calculate with.... ===

  * calculate e<sup>iπ</sup>
    * <key>Z</key> <key>SHIFT</key> <key>'e'<sup>x</sup></key>
    * '' - 1 + j 0 ''
    * e<sup>iπ</sup> = -1


==== Parallel Impedances ====

This involves the ''complex inverse'' function <key>Z</key> <key>1/x</key>

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



==== convert to Rectangular ⇔ Polar operation ====

  * ''Z = 50 - j 23'' 
  * initially in rectangular form...((<key>Z</key> <key>Z</key> <key>5</key> to make sure!))
    * enter Z as usual
      * <key>50</key> <key>Z</key> <key>XEQ</key> <key>23</key><key>CHS</key> <key>ENTER</key> 
    * convert to Polar format
      * <key>Z</key> <key>Z</key> <key>6</key> ( **6** is ''R->P'' but needs **two** presses of <key>Z</key> to activate it)
      * ''55.04 ∠ -24.70''
    * convert back to Rectangular operation
      * <key>Z</key> <key>Z</key> <key>5</key>
      * ''50 - j 23''

==== enter a number directly in Polar format ====

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


==== Cubic Roots of -8 ====

===Rectangular===

  * enter complex ''real'' number ''-8 + j 0''
    * <key>8</key> <key>CHS</key> <key>Z</key> <key>Z</key> <key>RCL</key>
      * '' -8 + j 0''
    * enter <key>3</key> (''goes into the normal X register'')
    * find the result of ''Z↑1/x''
      * <key>Z</key><key>Z</key><key>EEX</key>
        * ''1 + j 1.732''  (the first of the cube-roots of -8)
    * find the next root with the function ''ZNXTNRT''
      * <key>Z</key><key>Z</key><key>SHIFT</key><key>'√x'</key>
      * enter <key>3</key> at the ''_'' prompt
        * ''-2 + j 0''
    * find the next root with the function ''ZNXTNRT''
      * <key>Z</key><key>Z</key><key>SHIFT</key><key>'√x'</key>
      * enter <key>3</key> 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''
    * <key>8</key> <key>CHS</key> <key>Z</key> <key>Z</key> <key>RCL</key>
      * '' -8 + j 0''
      * convert to POLAR
        * <key>Z</key><key>Z</key><key>6</key>
          * ''8 ∠ 180''
    * enter <key>3</key> (''goes into the normal X register'')
    * find the result of ''Z↑1/x''
      * <key>Z</key><key>Z</key><key>EEX</key>
        * ''2 ∠ 60.000''  (the first of the cube-roots of -8)
    * find the next root with the function ''ZNXTNRT''
      * <key>Z</key><key>Z</key><key>SHIFT</key><key>'√x'</key>
      * enter <key>3</key> at the ''_'' prompt
        * ''2 ∠ 180''
    * find the next root with the function ''ZNXTNRT''
      * <key>Z</key><key>Z</key><key>SHIFT</key><key>'√x'</key>
      * enter <key>3</key> 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// <key>ENTER</key>
  * key real part (and no ENTER)
  * do ''complex enter'' (<key>Z</key> <key>ENTER</key>) or another ''complex function'' (e.g. <key>Z</key> <key>+</key>) (be careful with the stack lift or it gets confusing)
  * e.g. ''52 + j 36''
    * <key>36</key> <key>ENTER</key> <key>52</key> <key>Z</key> <key>ENTER</key>
    * ''52 + j 36'' is now in Stack
  * enter second number 
  * e.g. ''23 - j 15''
    * <key>15</key> <key>CHS</key> <key>ENTER</key> <key>23</key> (**don't** <key>Z</key> <key>ENTER</key> this...!!)
  * to add them together use <key>Z</key> <key>+</key> now (instead of <key>Z</key> <key>ENTER</key>)
  * result : ''75 + j 21''
 
===gotcha===

  * pressing <key>Z</key> <key>ENTER</key> 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 <key>Z</key> <key>+</key> 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: ~~LASTMOD~~


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