(42S) Roots of Complex Numbers
12-30-2019, 04:47 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,146 Joined: Dec 2013
(42S) Roots of Complex Numbers
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
Code:
 00 { 108-Byte Prgm } 01▸LBL "CROOTS" 02 RAD 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)