## Wednesday, July 6, 2016

### 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.

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