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.