DM41X 41z Module

• 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

• 41z_bs_2x2_2_1_.zip

• 41z_deluxe_manual_1_.pdf

ZK?YN Info

• 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.

• 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

• 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

• 2.75 + j 0
  • 2.75 Z Z RCL

• 0 + j 3.1415 (i Pi)
  • SHIFT π Z Z XEQ

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

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 = 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

• 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

• 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

• 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

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

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

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.

The natural entry mode is much better

1. you enter the real and imaginary parts in the order you expect them
2. the stack operation is less obscure.
3. 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