# Complex numbers

• Mar 20th 2008, 01:41 PM
math sucks
Complex numbers
Let $\displaystyle a_0=a_1=1$ and $\displaystyle a_n=a_{n-2}+ia_{n-1}$ for $\displaystyle n>1$.
Find $\displaystyle a_{2008}$
• Mar 20th 2008, 01:48 PM
mathceleb
Excel ran out of number spaces, but here is a start:
• Mar 20th 2008, 02:05 PM
math sucks
Quote:

Originally Posted by mathceleb
Excel ran out of number spaces, but here is a start:

How are you getting those numbers? Note that $\displaystyle i$ here stands for the imaginary unit, $\displaystyle i=\sqrt{-1}$
• Mar 20th 2008, 02:24 PM
Plato
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.
• Mar 20th 2008, 03:20 PM
mathceleb
Quote:

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

(Crying)

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