Register to reply 
Generating full sequence with complex numbers. 
Share this thread: 
#1
Feb2112, 10:40 PM

P: 41

Hello everyone,
I need some help with the following: I understand that by using x_{n} = ax_{n1}+b we can generate a full sequence of numbers. For example, if x_{1}=ax_{0}+b, then x_{2} = ax_{1}+b = a^{2}x_{0}+ab+b, and so on and so forth to x_{n}. I need help applying this same concept to complex numbers (a+bi). Is it even possible? I think it is, but I can't figure it out. Can some one lend a hand? 


#2
Feb2212, 04:48 AM

Sci Advisor
HW Helper
Thanks
P: 26,157

hello smithnya!
this is a recurrence relation its solutions should be of the same form, whether the constants are real or complex were you having a problem with any particular relation? 


#3
Feb2212, 09:20 AM

P: 41

Well, my professor began to explain the relation among real numbers, and he explained for x_{0}, x_{1}, x_{2}, etc. He mentioned that the same could be done with complex numbers, but never went into detail, maybe he will explain later. It piqued my curiosity, but I can't figure out how to generate a full sequence using the same method above only with something of the form a+bi.



#4
Feb2212, 09:59 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,345

Generating full sequence with complex numbers.
As tiny tim said, it is exactly the same thing: [itex]x_{n+1}= ax_n+ b[/itex] will give complex numbers if any one or more of a, b, and [itex]x_0[/itex] is complex.



Register to reply 
Related Discussions  
Generating function for r as sum of odd numbers, each of which occurs at most 3 times  General Math  0  
Generating functions and Recurrence relations using the Fibonacci sequence  Calculus & Beyond Homework  0  
Generating Kimberling Sequence  General Math  0  
Lucas Numbers and Generating Functions  Calculus & Beyond Homework  4  
Generating prime numbers  Linear & Abstract Algebra  12 