## Sunday, June 14, 2020

### TI-84 Plus CE: Complex Recurring Sequences

TI-84 Plus CE:  Complex Recurring Sequences

The program CMPXSEQ generates a matrix table for the complex recurring series:

C = (P + B * Q) / (1 + A)

where:
P and Q are complex constants
A = z_0
B = z_1
C = z_2

Restated, this recursion series becomes:

z_2 = (P + z_1* Q) / (1 + z_0)

In its current operating system (5.4.0), the TI-84 Plus CE's recurring sequence graphing mode cannot accept complex numbers.   Therefore a program is required.  Furthermore, matrices on the TI-84 Plus CE do not handle complex numbers.   It is required to break the complex numbers into parts.   For completeness I added both the rectangular and the polar parts of complex numbers:  real part, imaginary part, radius, and angle (dependent on angle mode).

TI-84 Plus CE Program CMPXSEQ  (text)

"EWS 2020-04-28"
ClrHome
a+bi
Disp "C=(P+B*Q)/(1+A)","COMPLEX","C=Z(N), B=Z(N-1), A=Z(N-2)"
Prompt P,Q
Input "Z0?",A
Input "Z1?",B
Input "NO OF STEPS?",N
{5,N+1}→dim([E])
For(I,0,N)
(P+Q*B)/(1+A)→C
I→[E](1,I+1)
real(C)→[E](2,I+1)
imag(C)→[E](3,I+1)
abs(C)→[E](4,I+1)
angle(C)→[E](5,I+1)
B→A
C→B
End
[E]^T→[E]
Disp "RESULT = [E]","[REAL,IMAG,ABS,ANGLE]"

Results are stored in matrix E.  ^T is the transpose function.

Examples

Tables generated using the LibreOffice Numbers desktop app and results verified with the TI-84 Plus CE.

Example 1:
P = 1
Q = i
z_0 = A = 2i
z_1 = B = -2

Example 2:
P = -i
Q = 1
z_0 = A = 2i
z_1 = B = -2

Example 3:
P = 1-i
Q = 1+i
z_0 = A = 2i
z_1 = B = -2

Have a great Sunday and week,

Eddie

All original content copyright, © 2011-2020.  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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