5: Brief review of complex analysis

Is it not amazing that complex numbers can be used for physics? Robert Musil (an Austrian novelist and mathematician), in “Verwirrungen des Zögling Törleß”, has expressed the amazement of a youngster confronted with the applicability of imaginaries, by stating that, at the beginning of any computation involving imaginary numbers are “solid” numbers which could represent something measurable, like lengths or weights, or something else tangible; or are at least real numbers. At the end of the computation, there are also such “solid” entities. But the beginning and the end of the computation are connected by something seemingly nonexisting. Does this not appear, Musil’s Zögling Törleß wonders, like a bridge crossing an abyss with only a bridge pier at the very beginning and one at the very end, which could nevertheless be crossed with certainty and securely, as if this bridge would exist entirely…