Find the curl of the vector field G Find the curl of the vector field:
$\underline{G}=(8r^7x-5r^3y)\underline{i}+(-8r^7y+5r^3x)\underline{j}$
where $r=(x^2+y^2)^\frac{1}{2}$
Since r is in the vector field, does it require calculation in polar coordinates? I am a bit confused with how to approach this.

This problem is actually pretty simple and doesn't need to use polar coordination system. 
Let $$\vec G = f(x,y)\vec i + g(x,y)\vec j$$ where $$ f(x,y) = 8 r^7x -5r^3y$$ $$ g(x,y) = -8 r^7y +5r^3x$$
$$curl \vec G = (\frac{\partial g(x,y)}{\partial x}-\frac{\partial f(x,y)}{\partial y})\vec k = 10r^3\vec k$$
