[T240722]证明:\(p,q\)为互质的整数\(\Longrightarrow\forallz\in\C,~(\sqrt[q]z)^p=\sqrt[q]{z^p}\).若\(p,q\)的最大公因数\(d>1\),结论如何?证：设\(p,q\in\mathbb{Z}\andp\perpq,~~z=r(\cos\theta+\mathrmi\sin\theta)\),则\[\begin{aligned}