Question

The value of \[ \int_{0}^{2+i}\left(\frac{\bar z}{2}\right)^2dz \] along \(x=2y\), is

• A. \(\dfrac{5}{3}(2+i)\)
• B. \(\dfrac{5}{3}(2-i)\)
• C. \(\dfrac{2}{3}(5-i)\)
• D. \(\dfrac{2}{3}(5+i)\)

Hint:

For complex line integrals, \[ \boxed{ z=x+iy,\qquad \bar z=x-iy } \] Always parameterize the given path first and then substitute \(z,\bar z,\,dz\).

Answer 1

The Correct Option is B