Compute the following line integral:
∫_{γ}(z²+3z+4)dz, where _{γ} is the circle |z|=2 oriented counter-clockwise.
--Taking a Complex Variables course and I am completely lost, and there is no solution manual, or answers at the back of the book for even #s!
I presume that you know that a complex number can be written in the form where r is |z|, the distance from the origin ( 0) to the given point and is the "argument", that angle the line from the origin to z makes with the positive real axis (positive x axis). If z= a+ ib, the , .
The point is that any point on "the circle |z|= 2" can be written so . . The "oriented counter-clockwise" means the integral is from 0 to .