Draw N random points from a unit circle

So I used the below code to draw a random point (between 0 and 1) from a unit circle . The code outputs 1 point at a time. So, if I want 5 different points I run the code for 5 times. What I want is to draw N different points (lets say about 1000). Is there a way that I can use for the purpose?

public class UniformPoint {
    public static void main(String[] args) {
        double t = (2 * Math.PI)*Math.random();
        double u = Math.random() + Math.random();
        double r;
        double x, y;
        if(u > 1){
            r = 2 - u;
        }
        else{
            r = u;
        }
        x = (r * Math.cos(t));
        y = (r * Math.sin(t));
        System.out.println("("+x+", "+y+")");
    }
}