Given an integer n≥ 2 and z0 ∈ C, consider the equation zn = z0. What are the n-th roots of z0?

The n-th roots of z0 are given by zk = n√r(cosϕk+ ...

Question

Given an integer n≥ 2 and z0 ∈ C, consider the equation zn = z0. What are the n-th roots of z0?

The n-th roots of z0 are given by zk = n√r(cosϕk+ isenϕk), where r is the modulus of z0, ϕk = θ +2kπ/n, and k = 0, 1, ..., n-1.
There are no other n-th roots of z0.

Ed · Answer

A pergunta está correta. A resposta é que as raízes n-ésimas de z0 são dadas por zk = n√r(cosϕk+ isenϕk), onde r é o módulo de z0, ϕk = θ +2kπ/n, e k = 0, 1, ..., n-1. Não há outras raízes n-ésimas de z0.

Given an integer n≥ 2 and z0 ∈ C, consider the equation zn = z0. What are the n-th roots of z0? The n-th roots of z0 are given by zk = n√r(cosϕk+ ...

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