Proving/Creating a conjecture on the roots of complex numbers

[Daaniyaal]

λ ε {2 π k/k}k=0∞

 

[tiny-tim]

where's n ?

 

[Daaniyaal]

where's n ?

Oh woops θ ε {2nkπ/n}k=0∞

 

[tiny-tim]

now, too many n's !

 

[Daaniyaal]

AAAAAAH. I swear there's a lot wrong up there. θ ε {2nkπ/k}k=0∞

 

[tiny-tim]

erm …

too many k's ?​

 

[Daaniyaal]

θ ε {2nkπ/k}k=0∞

 

[tiny-tim]

that's the same as your last one

(and 2nkπ/k = 2nπ))

 

[Daaniyaal]

2kpi/n ? I think I'm lost.

 

[tiny-tim]

yes, θ = (2π/n) times k, for any integer k, are the solutions to cos(nθ) = 1

(they're also the solutions for e^inθ = 1 … they correspond to n equally-spaced positions on the unit circle)

is that the answer to the original question? ​

 

[Daaniyaal]

Yes! How would I prove it though? :/

 

[Daaniyaal]

Algebraically, I already have the graph.

 

[tiny-tim]

Yes! How would I prove it though? :/

which part of the proof are you not clear about?

 

[Daaniyaal]

I figured it out, if I were to just replace the statement with my conjecture it would be proven, thanks!