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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?

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    http://math.stackexchange.com/questions/39567/for-a-polynomial-pz-prove-there-exist-r0-such-that-if-z-r-then-p2012-02-29

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