Complex Analysis: Theory and Applications · Problem 6.2.2

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · contour-sketching

Problem

Sketch the following curves. (a) z(t)=t2−1+i(t+4)z(t) = t^2 - 1 + i(t+4), for 1≤t≤31 \leq t \leq 3. (b) z(t)=sin⁡t+icos⁡2tz(t) = \sin t + i\cos 2t, for −π2≤t≤π2-\dfrac{\pi}{2} \leq t \leq \dfrac{\pi}{2}. (c) z(t)=5cos⁡t−i3sin⁡tz(t) = 5\cos t - i3\sin t, for π2≤t≤2π\dfrac{\pi}{2} \leq t \leq 2\pi.

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