Complex numbers

**math sucks** · March 20th 2008, 01:41 PM

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

**mathceleb** · March 20th 2008, 01:48 PM

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

**math sucks** · March 20th 2008, 02:05 PM

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, $i=\sqrt{-1}$

**Plato** · March 20th 2008, 02:24 PM

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.

**mathceleb** · March 20th 2008, 03:20 PM

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.

Check your PM.

Thread: Complex numbers