Generating full sequence with complex numbers.by smithnya Tags: complex, generating, numbers, sequence 

#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

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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

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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.



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