Complex Analysis: Theory and Applications · Problem 6.2.16

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · contour-parametrization

Problem

Let z(t)=x(t)+iy(t)z(t) = x(t) + iy(t), for a≤t≤ba \leq t \leq b, be a smooth curve. Give a meaning for each of the following expressions. (a) z′(t)z'(t). (b) ∣z′(t)∣ dt\left|z'(t)\right|\,dt. (c) ∫abz′(t) dt\displaystyle\int_a^b z'(t)\,dt. (d) ∫ab∣z′(t)∣ dt\displaystyle\int_a^b \left|z'(t)\right|\,dt.

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