Question

Calculate using Cauchys integral formula

Answer 1

Answer:

9πi/2

Step-by-step explanation:

$\oint\limits_C {\frac{5z^{2}+4}{(z-1)(z+3)} } \, dz,\ C: |z|=2$

Let f(z) = (5z² + 4) / (z + 3).

$\oint\limits_C {\frac{f(z)}{z-1} } \, dz,\ C: |z|=2$

Using Cauchy's integral formula:

$2\pi i\ f(1)\\2\pi i\ (\frac{5(1)^{2}+4}{1+3}) \\2\pi i\ (\frac{9}{4}) \\\frac{9\pi i}{2}$