# Boards

## Anyone fancy some late night maths?

Let w be a complex number such that w^7 = 1 and w =/= 1. Set t = w + w^2 + w^4. Find a quadratic with coefficients in Q which is satisfied by t.

It's driving me crazy :(

Let w be a complex number such that w^7 = 1 and w =/= 1. Set t = w + w^2 + w^4. Find a quadratic with coefficients in Q which is satisfied by t.

It's driving me crazy :(

## 0

## 1

## At GCSE, it actually is

Oh God, please someone help me.

## well w^7 and w =/= 1

->

quadratic = 16

## 16 isn't a quadratic

## oh sorry I mean 3

## hi

I would do this: write the equation as

Now swap x and t:

That "gives" the inverse function. Now you "only" have to solve for x!

Multiply that denominator on both sides:

Multiply the entire equation by ex

Let y= e^x so that you get a quadratic in y

Solve that by a simple square root, then take ln of both sides to find x as a function of x.

## ...

## sorry

it felt like i was being funny

## The worst thing is

it took me 5 minutes to work out you were taking the piss :(

## yeah sorry about that

i was going to fill whole page with some really length one with wacky signs but that fell through, so i copied some answer from a gcse website.

i hadn't planned on it looking even slightly like i was giving a real answer

## i haven't done maths for 3 months

i have forgotten all of it.

## Depressingly

## Friday

It's not like this is a question I need to know stuff for, I just need to be good at maths, and I'm evidently really, really not :|

## Nup

## no and never

## e