Teaching DSSSB TGT Mock Test 2025 Engineering Mathematics Complex Variables Cauchy's Integral Theorem
Let f be a meromorphic function on an open set containing the unit circle C and its interior. Suppose that f has no zeros and no poles on C, and let np and no denote the number of poles and zeros of f inside C, respectively. Which one of the following is true?
1
\(\frac{1}{2 \pi i} \int_C \frac{(z f)^{\prime}}{z f} d z=n_0-n_p+1 .\)
2
\(\frac{1}{2 \pi i} \int_C \frac{(z f)^{\prime}}{z f} d z=n_0-n_p-1 .\)
3
\(\frac{1}{2 \pi i} \int_C \frac{(z f)^{\prime}}{z f} d z=n_0-n_p .\)
4
\(\frac{1}{2 \pi i} \int_C \frac{(z f)^{\prime}}{z f} d z=n_p-n_0 .\)