Thread: roots

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

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.

Originally Posted by franios

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

Do you mean

Yes

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

Originally Posted by franios

Yes

Then .

The four fourth roots are