TI55 III Programs Part I: Digital Root, Complex Number Multiplication, Escape
Velocity
This blog begins a three part series of programs with the TI55 III. Let's show what this calculator can do.
For Part III: Area and Eccentricity of Ellipses, Determinant and Inverse of 2x2 Matrices, Speed of Sound/Principal Frequency
TI55 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 + ((n1) mod 9)
= n – 9 * integer((n1)/9)
Program:
Partitions Allowed: 15, 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
TI55 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:
24, 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

PR

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

PR

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

PR

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
TI55 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: 15
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