TI-55 III Programs Part I: Digital Root, Complex Number Multiplication, Escape Velocity

TI-55 III Programs Part I:  Digital Root, Complex Number Multiplication, Escape Velocity

This blog begins a three part series of programs with the TI-55 III.  Let's show what this calculator can do.

For Part II:  Impedance of a Series RLC Circuit, Quadratic Equation, Error Function

For Part III: Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2 Matrices, Speed of Sound/Principal Frequency

TI-55 III: Digital Root

Takes the digital root of an integer.  To find the digital root:

1.  Add up the number’s digits.

2.  The sum is over 10, add the digits again.

3.  Repeat step 2 until you get a single digit.

Or alternatively, use the formula dr(n) = 1 + ((n-1) mod 9) = n – 9 * integer((n-1)/9)

Program:

Partitions Allowed: 1-5, 1 register required

STEP	CODE	KEY	COMMENT
00	61	STO	Enter integer
01	00	0
02	75	-
03	09	9
04	65	*
05	53	(
06	53	(
07	71	RCL
08	00	0
09	75	-
10	01	1
11	54	)
12	55	÷
13	09	9
14	54	)
15	88	Intg
16	95	=
17	12	R/S	Display digital root

Input:  integer [RST] [R/S]

Result:  digital root

Test 1:  Input: 1555, Result: 7

Test 2:  Input: 38267, Result: 8

TI-55 III: Complex Number Multiplication

(a + bi)*(c + di) = (r1*r2) * e^(i*(θ1 + θ2))

Where r1 ∠ θ1 is the polar form of a + bi and r2 ∠ θ2 is the polar form of c + di.

Program:

Partitions Allowed:  2-4, 2 memory registers are required

STEP	CODE	KEY	COMMENT
00	52	X<>Y	Start with a
01	12	R/S	Prompt for b
02	41	INV
03	57	P-R	Convert to Polar
04	61	STO
05	01	1
06	52	X<>Y
07	61	STO
08	00	0
09	12	R/S	Prompt for c
10	52	X<>Y
11	12	R/S	Prompt for d
12	41	INV
13	57	P-R	Convert to Polar
14	61	STO
15	85	+
16	01	1	STO+ 1
17	52	X<>Y
18	61	STO
19	65	*
20	00	0	STO* 0
21	71	RCL
22	00	0
23	52	X<>Y
24	71	RCL
25	01	1
26	57	P-R	Convert to Rectangular
27	12	R/S	Display imaginary part
28	52	X<>Y
29	12	R/S	Display real part

Input:  a [RST] [R/S], b [R/S], c [R/S], d [R/S]

Result:  imaginary part of the product [R/S], real part of the product

Test 1:  (5 – 3i)*(4 + i)

Input: 5 [RST] [R/S], 3 [+/-] [R/S], 4 [R/S], 1 [R/S]

Result: -7 [R/S] 23   (23 – 7i)

Test 2: (-6 + 3i)*(2 + 2i)

Result:  -18 – 6i

TI-55 III:  Escape Velocity

v = √(2*G*m/r)

v = escape velocity (m/s)

G = University Gravitational Constant = 6.67384 * 10^-11 m^3/(kg*s^2)

m = mass of the planet (kg)

r = radius of the planet (m)

Note that 2*G = 1.334768 * 10^-10 m^3/(kg*s^2)

Program:

Allowed Partitions: 1-5

STEP	CODE	KEY	COMMENT
00	47	Eng	Set Engineering Mode
01	65	*	Start with mass
02	01	1
03	93	.	Decimal Point
04	03	3
05	03	3
06	04	4
07	07	7
08	06	6
09	08	8
10	42	EE
11	01	1
12	00	0
13	94	+/-
14	55	÷
15	12	R/S	Prompt for radius
16	95	=
17	13	√
18	12	R/S	Display escape velocity

Input:  mass (in kg) [RST] [R/S] radius (in m) [R/S]

Result: escape velocity (m/s)

Test 1:

Earth:  m = 5.97219 * 10^24 kg, r = 6.378 * 10^6 m

Input:  5.97219 [EE] 24 [RST] [R/S] 6.378 [EE] 6 [R/S]

Result:  ≈ 11.179E3 (11,179 m/s)

Test 2:

Jupiter:  m = 1.89796 * 10^27 kg, r = 71.492 * 10^6 m

Result:  ≈ 59.528E3  (52,528 m/s)

Eddie

This blog is property of Edward Shore, 2016