Question

Prove, or give a counter example to disprove the following statements.

a) $\forall f(x) \in \mathbb{C}[x], \exists \, z \in \mathbb{C}, f(z)=0\Rightarrow f(\bar{z})=0.$

b)$\forall \,k \in \mathbb{N}, \exists z \in \mathbb{C} \,\,such \,\,that\, z^{k}=1 \Rightarrow \forall \, d|k \, \,and \, \, d>1,$$\exists \, m \in \mathbb{Z} \; such \; that \; 1\leq m< k\; and \; (z^{m})^{d}=1$

Answer 1

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