# Generating full sequence with complex numbers.

1. Feb 21, 2012

### smithnya

Hello everyone,

I need some help with the following: I understand that by using xn = axn-1+b we can generate a full sequence of numbers. For example, if x1=ax0+b, then x2 = ax1+b = a2x0+ab+b, and so on and so forth to xn. 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. Feb 22, 2012

### tiny-tim

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. Feb 22, 2012

### smithnya

Well, my professor began to explain the relation among real numbers, and he explained for x0, x1, x2, 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. Feb 22, 2012

### HallsofIvy

Staff Emeritus
As tiny tim said, it is exactly the same thing: $x_{n+1}= ax_n+ b$ will give complex numbers if any one or more of a, b, and $x_0$ is complex.