Compute all the 4th roots of a=1+√3 & describe where they are located in the complex plane.

Printable View

- September 17th 2012, 10:34 AMfraniosroots
Compute all the 4th roots of a=1+√3 & describe where they are located in the complex plane.

- September 17th 2012, 10:49 AMemakarovRe: roots
According to the formula from another problem, [r , θ]ⁿ = [rⁿ, nθ]. If [r⁴, 4θ] = [1+√3, 0], then . You need to find all 0 ≤ θ < 2π such that 4θ is an integer multiple of 2π.

- September 17th 2012, 10:59 AMPlatoRe: roots
- September 17th 2012, 03:12 PMfraniosRe: roots
Yes

- September 17th 2012, 03:18 PMemakarovRe: roots
Well, the idea is the same, only now and you need to find all 0 ≤ θ < 2π such that 4θ equals arg(a) up to an integer multiple of 2π

- September 17th 2012, 03:26 PMPlatoRe: roots