## Monday, December 30, 2019

### HP 42S & DM42 Complex Roots (Happy New Year)

HP 42S & DM42 Complex Roots (Happy New Year)

Introduction

The program CROOTS calculates the roots of a complex number.

(a+bi)^n   (n is a positive integer).

The roots are determined by the formula:

(a + bi)^(1/n) =  r^(1/n) * e^(i * (θ + 2*k*π)/n)    (k = 0, 1, 2, ... , n-1)

The results are stored in matrix MATZ.  The calculator is switched to Radians mode during execution.

Stack when running CROOTS:

Y:  complex number
X:  n

HP 42 & DM42 Program CROOTS

00 { 108-Byte Prgm }
01▸LBL "CROOTS"
03 STO 01
04 R↓
05 STO "ZC"
06 1
07 RCL 01
08 NEWMAT
09 ENTER
10 COMPLEX
11 STO "MATZ"
12 RCL 01
13 1
14 -
15 1ᴇ3
16 ÷
17 STO 02
18 INDEX "MATZ"
19 RCL "ZC"
20 COMPLEX
21 X<>Y
22 →POL
23 RCL 01
24 1/X
25 Y↑X
26 STO 03
27 R↓
28 STO 04
29▸LBL 01
30 RCL 04
31 2
32 PI
33 ×
34 RCL 02
35 IP
36 ×
37 +
38 RCL÷ 01
39 0
40 ENTER
41 1
42 COMPLEX
43 ×
44 E↑X
45 RCL 03
46 ×
47 1
48 RCL 02
49 IP
50 1
51 +
52 STOIJ
53 R↓
54 R↓
55 STOEL
56 ISG 02
57 GTO 01
58 EDITN "MATZ"
59 .END.

Example
(FIX 4 mode)

Find the three roots of 5+4i.   (5+4i)^(1/3)

Y:  5.0000 i4.0000
X:  3

Result:
1:1=1.8102 i0.4141
1:2=-1.2637 i1.3606
1:3=-0.5464 -i1.7747

(approximately 1.8102+0.4141i, -1.2637+1.3606i, -0.5464-1.7747i)

I want to wish every one a fun, happy, and safe New Year's Celebration.  Thank you for joining me this year and I wish you a happy, healthy, and prosperous 2020!

HAPPY NEW YEAR!

See you on January 4, 2020,

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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