Simplify 4 over quantity 2 plus 7 i.

To simplify 4/(2+7i), we multiply it by a fraction equal to one that removes the i value in the denominator.  The best value to do this is the complex conjugate divided by itself, so we have 4(2-7i)/((2+7i)(2-7i)).  Simplifying, we have (8-28i)/(4-(-49))=(8-28i)/53, which is a completely simplified fraction since 8 and 53 are relatively prime (or coprime), and there are no radicals in the denominator.