You are Here: Home >< Maths

# Simplify powers of conjugates? Maths Help watch

1. For example, is there an easy way to simplify (1+sqrt(3))^n - (1-sqrt(3))^n ???
Both to the same power, just conjugates of each other and one being subtracted from the other... Can this be simplified?
2. (Original post by ComputerMaths97)
For example, is there an easy way to simplify (1+sqrt(3))^n - (1-sqrt(3))^n ???
Both to the same power, just conjugates of each other and one being subtracted from the other... Can this be simplified?
Well if
and

Then what does that suggest?
3. (Original post by Aph)
Well if
and

Then what does that suggest?
From what you've said, it seems that every odd nth term would double and each even nth term would cancel since we're subtracting the second from the first. This leaves the answer as a multiple of sqrt(3).

Since I posted this question, I've managed to get that:

If

Then where k = n + 1

And exact same applied for conjugate, just a minus sign before the sqrt(3) term.

But this doesn't really seem to help me any further.

EDIT : Got an Update - posting it below, gimme a sec to type it out.
4. Aph

Update:

Got this:

If

Then where k = n + 1

So does this mean we have a common difference of
? Seems like it, now I just need to find a way of evaluating this in more detail.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 26, 2015
Today on TSR

### Congratulations to Harry and Meghan!

But did you bother to watch?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams