Argand diagram with roots of unity

[high fable]

@vale crow

[vale crow]

the fuck i got pinged directly

ahhhhhh this looks painful

[vale crow]

ok so

any thoughts?

[high fable]

Well I did the cube roots of unity

[vale crow]

yep so

well like what about them did you do

[high fable]

Then I found midpoints

[vale crow]

ok yep

[high fable]

But idk how to make it a polynomial

[vale crow]

ok so

well you know with like not complex roots

like if i say it has a root at 1

you can say (x-1) is a root

yeah?

[high fable]

Ye

[vale crow]

so you can do the same with complex numbers

[high fable]

Ohhh

[vale crow]

if e^(2i pi /3) is a root

[high fable]

I see

[vale crow]

(z - e^(2i pi/3)) is a factor

now i iwll say

while this is perfectly good

its a massive pain in the arse

but you could just find all the roots and expand and shit

theres a faster way tho:

so do you know what the roots of unity are for

like where are they from

[high fable]

Thanks ❤️

[vale crow]

see the text i posted plsss

itll speed things u pfor you

@high fable

[high fable]

You mean the coordinates?

Or wdym

[vale crow]

as in where do you generate them from

what im saying is that

you know the roots of unity are from

z^n = 1 right

[high fable]

Ye

[vale crow]

so the cube roots of unity are z^3 = 1

[high fable]

Ye

[vale crow]

well if you say thats the same as

z^3 - 1 = 0

so you know z^3 - 1 could be. afactor

and thatll already give you the 3 roots

so its (z^3 - 1)(stuff) = 0

where the z^3 - 1 gives you the 3 cube roots of unity