int x, y, xx, yy; // Why are these variables here? I don't know what they mean. They should be declared where you use them, not here.
	double radians; // Same thing. At least this one has a better name. Although it's only the units...
	list<Vertex>::iterator itr = vertices.begin(); // One would normally put this line and the two marked with (*) in a single for loop.
	while (itr != vertices.end()) // (*)
	{
		x = centroid.getX(); // This would be a good place to declare the type of x. But the value you are assigning never gets used.
		y = centroid.getY();


		x = vertices.back().getX() - centroid.getX(); // Oh, so this is what you wanted x to be.
		y = vertices.back().getY() - centroid.getY();

		radians = degrees * PI / 180; // If degrees doesn't change inside the loop, why is this computation inside the loop?
		xx = round(x * cos(radians) - y * sin(radians)); // And why are you using integer coordinates? Rotation wonn't work too well..
		yy = round(y * cos(radians) + x * sin(radians));
		xx = xx + centroid.getX(); // Here you are modifying xx, which means the variable meant something up to this point, and something different from now on.
		yy = yy + centroid.getY();
		vertices.push_back(Vertex(xx, yy));

		itr++; // (*) It's probably better to use ++itr, but you are not ready to understand why, so don't worry about it too much for now.
	}

}

I now get no output to the console?

#include <iostream>
#include <vector>
#include <complex>

typedef std::complex<float> C;

std::vector<C> rotate_points(std::vector<C> const &points, float angle, C center_of_rotation) {
  std::vector<C> result;
  C rotation = std::polar(1.0f, angle);
  for (auto point : points)
    result.emplace_back(center_of_rotation + (point - center_of_rotation) * rotation);
  return result;
}

const float TAU = std::atan(1.0f) * 8.0f;

int main() {
  std::vector<C> points = {C(1.0f, 1.0f), C(-2.0f, -1.0f)};
  float angle = TAU * 0.25f; // A quarter of a turn, a.k.a. 90 degrees
  std::vector<C> rotated_points = rotate_points(points, angle, C(1.0f, 1.0f));
  for (auto point : rotated_points)
    std::cout << point << '\n';
}

Just for fun...

Dammit, why did I never learn cool properties of complex numbers when I was in school?!

Here, free code commentary. Don't get used to it, though; Nypyren is absolutely right that you should learn to go through the code yourself, either executing the code by hand or with the help of a debugger.

	int x, y, xx, yy; // Why are these variables here? I don't know what they mean. They should be declared where you use them, not here.
	double radians; // Same thing. At least this one has a better name. Although it's only the units...
	list<Vertex>::iterator itr = vertices.begin(); // One would normally put this line and the two marked with (*) in a single for loop.
	while (itr != vertices.end()) // (*)
	{
		x = centroid.getX(); // This would be a good place to declare the type of x. But the value you are assigning never gets used.
		y = centroid.getY();


		x = vertices.back().getX() - centroid.getX(); // Oh, so this is what you wanted x to be.
		y = vertices.back().getY() - centroid.getY();

		radians = degrees * PI / 180; // If degrees doesn't change inside the loop, why is this computation inside the loop?
		xx = round(x * cos(radians) - y * sin(radians)); // And why are you using integer coordinates? Rotation wonn't work too well..
		yy = round(y * cos(radians) + x * sin(radians));
		xx = xx + centroid.getX(); // Here you are modifying xx, which means the variable meant something up to this point, and something different from now on.
		yy = yy + centroid.getY();
		vertices.push_back(Vertex(xx, yy));

		itr++; // (*) It's probably better to use ++itr, but you are not ready to understand why, so don't worry about it too much for now.
	}

}

I now get no output to the console?

What output did you expect? I didn't see any line of code in what you posted that printed anything.

Great advice thank you very much, what you commented on really made sense.To output I call a drawshape function which plots the vertices from the vertex list.

As you can see from the code above I use push back to add the rotated vertices to the list and then re draw the shape with the draw shape function with the newly defined vertices, what I mean by no output is I draw the shape, which display the shape, rotate the vertices using the rotate function, clear the console to re draw but when I re draw nothing appears like it cant find the newly defined vertices.

As you can see from the code above I use push back to add the rotated vertices to the list and then re draw the shape with the draw shape function with the newly defined vertices, what I mean by no output is I draw the shape, which display the shape, rotate the vertices using the rotate function, clear the console to re draw but when I re draw nothing appears like it cant find the newly defined vertices.

I have narrowed it down to being an issue with the push back in the rotate function.

I have created a function to output the vertices before the rotate function and everything is as expected.

Once I introduce rotation, with the push back on the vertex list, the program hangs like its stuck in the while loop (now a for loop).

Should I be creating a separate list to hold the newly rotated x and y?

I have narrowed it down to being an issue with the push back in the rotate function.

I have created a function to output the vertices before the rotate function and everything is as expected.

Once I introduce rotation, with the push back on the vertex list, the program hangs like its stuck in the while loop (now a for loop).

Should I be creating a separate list to hold the newly rotated x and y?

Scratch that, I was getting caught in an infinite look because I was starting at the begin() of list instead off end(), so I would increment forward and then push back thus getting stuck if I'm correct. Now i start at the end() and -- and get my output of added x and y to my list.