RPN with HP 15C and DM32: Complex Mode
HP
15C Complex Mode
This
section also
applies to the Swiss Micros DM15 family.
Complex
mode is a separate mode for the HP 15C. Complex mode is turned on
by setting flag 8. Complex mode is on when there is a “C”
indicator in the display.
In
complex mode, the stack is expanded. Each stack level now includes a
real part and a complex part. What is in the display is always the
real part.
Stack T
|
Real part of T
|
Imaginary part of T
|
Stack Z
|
Real part of Z
|
Imaginary part of Z
|
Stack Y
|
Real part of Y
|
Imaginary part of Y
|
Stack X
|
Real part of X
|
Imaginary part of X
|
The
great news is that the stack handles up to four complex numbers, one
for each of the stack levels.
To
display the imaginary part, we have two methods:
Temporary
View: Press [ f ] and hold
[ COS ] (i) to temporarily view the complex part. The stack remains
unaffected.
Switch:
Switch the real part and the imaginary part by pressing [ f ] [ - ]
(Re<>Im). Doing this switches the real and imaginary parts of
the X stack.
For
example: X = 9 – 8i
Enter
the complex number as such: 9 [ ENTER ] 8 [ CHS ] [ I ] * (see
note).
The
displays shows 9.
Press
[ f ] [ - ] (Re<>Im). The display shows -8 and the X stack
now has the complex number X = -8 + 9i.
Press
[ f ] [ - ] (Re<>Im) to switch the parts back to the original
complex number.
*
Note: If complex mode is
turned off (no C indicator), using this key sequence sets flag 8,
turning on complex mode automatically.
The
switching of parts is important, because memory registers can not
hold an entire complex number, but it’s separate parts. Thus, we
will need two registers, one for the real part and one for the
imaginary part.
HP
15C: Leaving Complex Mode
To
leave complex mode, clear flag 8 (CF 8). The imaginary parts of the
stack are lost.
Angle
Mode
In
complex mode, the trigonometric functions operate as the angles are
always in radian measure regardless of the angle setting. The only
functions that recognize the angle setting are the polar/rectangular
conversions. To take the cosine and sine of angle that respects
the conversion, use the following sequence:
angle
[ENTER] 1 [ f ] [ →R ]: X stack: cos(angle), Y stack:
sin(angle)
HP
15C - Solving Monic Quadratic Equations
The
HP 15C’s solver only works for real numbers, so manual methods and
formulas must be used to solve equations for complex numbers.
Z^2
+ w1 * Z + w0 = 0
Solution:
Z = (w1 ± √(w1^2 – 4 * w0)) / 2
(D
= √(w1^2 – 4 * w0), Z+ = (w1 + D) / 2 Z- = Z+ - D)
Store
the following:
Complex
coefficient w1: Real part in register 4, Imaginary part in register
5
Complex
coefficient w2: Real part in register 1, Imaginary part in register
2
The
results are stored in the following registers:
Discriminant
(D): Real part in register 6, imaginary part in register 3
Complex
root Z+: Real part in register .0 (decimal point-0), imaginary
party in register 8
Complex
root Z-: Real part in register 9, imaginary part in register 7
Code
(use any label you want, I use label A for example):
Key
|
Key Code
|
|
Key
|
Key Code
|
LBL A
|
42, 21, 11
|
|
RCL 4
|
45, 4
|
SF 8
|
43, 4, 8
|
|
RCL 1
|
45, 1
|
RCL 4
|
45, 4
|
|
I
|
42, 25
|
RCL 1
|
45, 1
|
|
-
|
30
|
I
|
42, 25
|
|
2
|
2
|
x^2
|
43, 11
|
|
÷
|
10
|
RCL 5
|
45, 5
|
|
STO .0
|
44, .0
|
RCL 2
|
45, 2
|
|
Re<>Im
|
42, 30
|
I
|
42, 25
|
|
STO 8
|
44, 8
|
4
|
4
|
|
Re<>Im
|
42, 30
|
×
|
20
|
|
R/S
|
31
|
-
|
30
|
|
RCL 6
|
45, 6
|
√
|
11
|
|
RCL 3
|
45, 3
|
STO 6
|
44, 6
|
|
I
|
42, 25
|
Re<>Im
|
42, 30
|
|
-
|
30
|
STO 3
|
44, 3
|
|
STO 9
|
44, 9
|
Re<>Im
|
42, 30
|
|
Re<>Im
|
42, 30
|
|
|
|
STO 7
|
44, 7
|
|
|
|
Re<>Im
|
42, 30
|
|
|
|
RTN
|
43, 32
|
Example:
Z^2
+ (4 + i) * Z + (2 - 5i) = 0
w1:
4 STO 4, 1 STO 1
w2:
2 STO 5, 5 CHS STO 2
[
f ] A or [ GSB ] A:
0.11724
[ f ] hold (i) 1.15309 (Z+ ≈ 0.11724 + 1.15309i)
[
R/S ]
-4.11724
[ f ] hold (i) -2.15309 (Z- ≈ -4.11724 – 2.15309i)
DM32
Complex Mode
This section also applies to the HP 32Sii, HP 32S, and the HP
41C/DM41X with the Advantage ROM plugged in. The names of the
functions vary.
There is no “separate” complex mode for the DM32, all the
functions are access with shifted CMPLX prefix function. The
complex number functions available on the DM32 are:
CMPLX+, CMPLX-, CMPLX×, CMPLX÷
CMPLX+/- (change sign, multiply the complex number by -1)
CMPLX1/x, CMPLXe^x, CMPLXLN, CMPLXy^x
CMPLXSIN, CMPLXCOS, CMPLXTAN
The complex functions grabs the values from the four stack levels and
uses them as up to two complex numbers:
Z
|
Imaginary part of T + Zi
|
T
|
Real part of T + Zi
|
Y
|
Imaginary part of X + Yi
|
X
|
Real part of X + Yi
|
Memory
registers can not hold an entire complex number, but it’s separate
parts. Thus, we will need two registers, one for the real part and
one for the imaginary part.
To
enter complex numbers, enter the imaginary part, press [ ENTER ],
then enter the real part.
Square
Root and Square (√ and x^2)
There is no complex square root or complex square function. We will
need some creativity to tackle these functions. Here is just one way
we can accomplish this task.
Assume the complex number A + Bi have the real part stored in A and
imaginary part stored in B.
Square Root (√):
RCL B
RCL A
0.5
ENTER
Clx
x<>y
CMPLXy^x
Square (x^2):
RCL B
RCL A
RCL B
RCL A
CMPLX×
Angle
Mode
In
complex mode, the trigonometric functions operate as the angles are
always in radian measure regardless of the angle setting. The only
functions that recognize the angle setting are the polar/rectangular
conversions. To take the cosine and sine of angle that respects
the conversion, use the following sequence:
1
[ENTER] angle [ blue shift ] [ →y,x ]: X stack: cos(angle), Y
stack: sin(angle)
(HP
32SII late editions: lavender/purple shift)
DM32
- Solving Monic Quadratic Equations
Like
the HP 15C, the DM32’s
solver only works for real numbers, so manual methods and formulas
must be used to solve equations for complex numbers.
Z^2
+ w1 * Z + w0 = 0
Solution:
Z = (w1 ± √(w1^2 – 4 * w0)) / 2
(D
= √(w1^2 – 4 * w0), Z+ = (w1 + D) / 2 Z- = Z+ - D)
Store
the following:
Complex
coefficient w1: Real part in A,
Imaginary part in B
Complex
coefficient w2: Real part in C,
Imaginary part in D
The
program will prompt for A, B, C, and D, in the order of imaginary
part, then real part
Z^2
+ (Bi + A) *
Z + (Di + C)
= 0
The
results are stored in the following registers:
Discriminant
(D): Real part in E,
imaginary part in F
Complex
root Z+: Real part in R,
imaginary party in S
Complex
root Z-: Real part in U,
imaginary part in V
Code:
A01 LBL A
|
A24 x<>y
|
A02 INPUT B
|
A25 RCL B
|
A03 INPUT A
|
A26 RCL A
|
A04 INPUT D
|
A27 CMPLX-
|
A05 INPUT C
|
A28 2
|
A06 RCL B
|
A29 ENTER
|
A07 RCL A
|
A30 CLx
|
A08 RCL B
|
A31 x<>y
|
A09 RCL A
|
A32 CMPLX÷
|
A10 CMPLX×
|
A33 STO S
|
A11 4
|
A34 x<>y
|
A12 RCL× D
|
A35 STO R
|
A13 4
|
A36 x<>y
|
A14 RCL× C
|
A37 STOP
|
A15 CMPLX-
|
A38 RCL F
|
A16 0.5
|
A39 RCL E
|
A17 ENTER
|
A40 CMPLX-
|
A18 CLx
|
A41 STO U
|
A19 x<>y
|
A42 x<>y
|
A20 CMPLXy^x
|
A43 STO V
|
A21 STO E
|
A44 x<>y
|
A22 x<>y
|
A45 RTN
|
A23 STO F
|
|
Example:
Z^2
+ (4 + i) * Z + (2 - 5i) = 0
[
XEQ ] A
B?
1 [R/S]
A?
4 [R/S]
D?
-5 (5 [+/-] ) [R/S]
C?
2 [R/S]
Y:
1.15309, X: 0.11724 (Z+ ≈ 0.11724 + 1.15309i)
[R/S]
Y:
-2.15309, X: -4.11724 (Z-
≈ -4.11724 – 2.15309i)
I
hope you enjoyed this edition of RPN with HP 15C and DM2,
Eddie
All
original content copyright, © 2011-2025. Edward Shore.
Unauthorized use and/or unauthorized distribution for commercial
purposes without express and written permission from the author is
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