(Solved): Phys 601 Exercises on Contour Integrals(1) 2. On Simple Contour Integrals: a. Find the integral of ...

Phys 601 Exercises on Contour Integrals(1) 2. On Simple Contour Integrals: a. Find the integral of $f(Z)=Z^n$ along the following paths: i. A straight line from $(0,0)$ to $(5,3)$ ii. From $(0,0)$ to $(5,0)$ on the $x$-axis and then from $(5,0)$ to $(5,3)$ parallel to the $y$-axis b. Find the integral of $1/Z^n$ along a semi-circular contour of radius 4 in the upper half of the Z-plane and then in the lower half of the Z-plane. c. Show that $?{?}_C\frac{dZ}{Z^2?1}??\frac{?}{3}$ where $C:?Z?=2$ from 2 to $2i$