Let $ a_n $ complex sequence prove that if $ a_n\to \infty$ then $ |a_n|\to\infty$ . Note that $ a_n = x_n + y_ni$ i dont know how to write that mathmatically.

trial :

Can i say that for every $ M>0$ there exist $ N$ such that for every $ n>N$ ,

$ ~~|x_n|>M~~ OR ~~~|y_n|>M$ ( At least one of them goes to $ \infty$ )

because of that $ |an| = \sqrt{(x_n)^2+(y_n)^2} > M$ and so $ |a_n|\to\infty$ .