Question

Evaluate \(\int_c \frac{z^2 - z + 1}{z - 1} dz\) where c is the circle (i) \(|z| = 1\) (ii) \(|z| = \frac{1}{2}\)

          Evaluate \(\int_c \frac{z^2 - z + 1}{z - 1} dz\) where c is the circle
(i) \(|z| = 1\)
(ii) \(|z| = \frac{1}{2}\)

Evaluate (z^2 - z + 1)/(z - 1) dz where c is the circle
(i) |z| = 1
(ii) |z| = (1)/(2)

Added by Carolina C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Narayan Hari

Step 1

We know that the equation of a circle with center (a, b) and radius r is given by (Z - a)^2 + (Z - b)^2 = r^2. In this case, the center is Z = 1 and the radius is |Z| = 1. So the equation becomes (Z - 1)^2 + (Z - 1)^2 = 1^2. Expanding this equation, we get Z^2 Show more…

Show all steps