The study of tangent cones in geometric analysis is an important tool in understanding the structure at a singular point of a geometric equation. In this talk I will discuss how to uniquely identify the tangent cone of a Yang-Mills connection with isolated singularity in the complex setting, given an initial assumption on the complex structure of the bundle. I will then discuss applications to a project with the goal of constructing examples of singular G2 instantons, using the twisted connected sum construction. This is joint work with H. Sa Earp and T. Walpuski.