I'm a student in Korea.
If I make a mistake in grammar, please indicate.

Recently, I'm studying the book 'Principles of Mathematical Analysis'
So, I tried to solve the exercise #2 in chapter 2.

'A complex number $z$ is said to be algebraic if there are integer $a\_0, \dots, a\_n$ ,not all zero, such that $a\_0 z^n + a\_1 z^{n-1} + \dots + a\_n =0$ '

The hint is 'For every positive integer $N$ there are only finitely many equation with $n+|a\_0|+...+|a\_n|=N$'

Of course, I have searched this exercise on this site. But there were different methods.

I want to prove this exercise by using the hint. please help me.