(a) Write f(z) in terms of partial fractions and integrate it counterclockwise over the unit circle, where

(b) In the light of the principle of deformation of path. Then consider another family of paths with common endpoints, say, z(t) = t + iα(t - t²), 0 ‰¤ t ‰¤ 1, α a real constant, and experiment with the integration of analytic and nonanalytic functions of your choice over these paths (e.g., z, Im z, z², Re z², Im z², etc.).

Transcribed Image Text:

2z + 3i (i) f(z) (ii) f(z) z? + 1 z2 + 2z