Let p be a complex polynomial $ p\left( {a + bi} \right) = p\left( z \right):{\Bbb C} \to {\Bbb C} $ How can I prove the following? $ \lim_{\lVert z\rVert\to\infty} \Vert p(z)\rVert = \infty.$
I can't use any important result about complex numbers, only the definition, and properties of $\mathbb{R}$ , how can I prove it?