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

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- Sep 17th 2012, 09:34 AMfraniosroots
Compute all the 4th roots of a=1+√3 & describe where they are located in the complex plane.

- Sep 17th 2012, 09:49 AMemakarovRe: roots
According to the formula from another problem, [r , θ]ⁿ = [rⁿ, nθ]. If [r⁴, 4θ] = [1+√3, 0], then $\displaystyle r=\sqrt[4]{1+\sqrt{3}}$. You need to find all 0 ≤ θ < 2π such that 4θ is an integer multiple of 2π.

- Sep 17th 2012, 09:59 AMPlatoRe: roots
- Sep 17th 2012, 02:12 PMfraniosRe: roots
Yes

- Sep 17th 2012, 02:18 PMemakarovRe: roots
Well, the idea is the same, only now $\displaystyle r=\sqrt[4]{|a|}$ and you need to find all 0 ≤ θ < 2π such that 4θ equals arg(a) up to an integer multiple of 2π

- Sep 17th 2012, 02:26 PMPlatoRe: roots