# Math Help - Complex numbers

1. ## Complex numbers

Let $a_0=a_1=1$ and $a_n=a_{n-2}+ia_{n-1}$ for $n>1$.
Find $a_{2008}$

2. Excel ran out of number spaces, but here is a start:

3. Originally Posted by mathceleb
Excel ran out of number spaces, but here is a start:
How are you getting those numbers? Note that $i$ here stands for the imaginary unit, $i=\sqrt{-1}$

4. This is known sequence with period of 12.
It repeats itself for each 12 just as i repeats every four.
Use mod(12) to get the answer.

5. Originally Posted by math sucks
How are you getting those numbers? Note that $i$ here stands for the imaginary unit, $i=\sqrt{-1}$

I thought $i$ was the number of the term, i.e., 1st term is 1, 2nd term is 2. -2 points for me, sorry about that.