If \( C \) is the unit circle in the complex plane with its center at the origin, then the value of \( n \) in the equation given below is (rounded off to 1 decimal place). \[ \int_C \frac{z^3}{(z^2 + 4)(z^2 - 4)} \, dz = 2 \pi i n \]
The directional derivative of the function \( f \) given below at the point \( (1, 0) \) in the direction of \( \frac{1}{2} (\hat{i} + \sqrt{3} \hat{j}) \) is (rounded off to 1 decimal place). \[ f(x, y) = x^2 + xy^2 \]