I thought i understood complex numbers and accepted them until I did countour integration for the first time.

Ever since then I have been deeply unsettled. I started questioning taking integrals to (+/-) infinity, and so I became unsettled with R too.

If C exists to fix R, then why does R even exist? Why does R need to be fixed? Why does the use of the upper or lower plane for counter integration not matter? I can do mathematically why, but why do we have a choice?

This blog post really articulated stuff formally that I have been bothered by for years.