How many roots does a system of polynomial equations have?

A polynomial of degree n with real coefficients has n complex roots.

How can one find out the number of complex roots of a system of two
polynomial equations in two variables?

Example:

x^3 - 3*y^2*x == 0 and x^2+y^2 - 4 == 0

I am not familiar with the topic, so sorry if this is a trivial/stupid
question. I was not able to figure it out on my own. Any pointers in
the right direction would be most appreciated.
.