<-[[..:]] ====== DM41X 41z Module ====== ===== Keyboard Overlay ===== {{ :public:calculator:guides:large_41z.png?400 |}} ===== 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 ==== Module ==== * {{ :public:calculator:guides:41z_bs_2x2_2_1_.zip |}} ==== User Guide ==== * {{ :public:calculator:guides:41z_deluxe_manual_1_.pdf |}} ==== 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 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 ZZ6 ''55.04 ∠ 24.70'' All further entries will remain as ''POLAR'' eg a new complex number in POLAR format ''100 ∠ - 85'' 100 ENTER 85CHS ENTER display : ''100 ∠ - 85'' Switch back to ''RECT'' mode ZZ5 ''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 ===== * 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...((Z Z 5 to make sure!)) * 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: ~~LASTMOD~~ {{tag>calculator dm41x}}