Evaluate HC2z+3z dz where C is upper half of the circle |z| = 2 in clockwise direction

To solve this problem, we will use the method of contour integration in complex analysis. Here are the steps:

1. Parameterize the contour: Since C is the upper half of the circle |z| = 2, we can parameterize it as z = 2e^(it) where -π ≤ t ≤ π.

2. Substitute z into the integral: We have HC2z + 3z dz = H(22e^(it) + 32e^(it)) * i2e^(it) dt = H(4e^(it) + 6e^(it)) * i2e^(it) dt = H(10e^(2it))i dt.

3. Evaluate the integral: ∫C HC2z + 3z dz = ∫ from -π to π H(10e^(2it))i dt.

4. Solve the integral: This is a standard integral and can be solved using techniques of calculus. The result will be a complex number.

Note: H is a function that needs to be specified. The steps above assume that H is a function that can be integrated in the standard way. If H is a more complex function, additional techniques may be needed to evaluate the integral.