Teaching CSIR NET Mock Test Series Mathematical Science Complex Analysis Theorems of Complex analysis
Let a, b be two real numbers such that a < 0 < b. For a positive real number r, define γr(t) = reit (where t ∈ |0, 2π|) and Ir = \(\rm \frac{1}{2\pi i}\int_{\gamma_r}\frac{z^2+1}{(z-a)(z-b)}dz\) Which of the following statements is necessarily true?
1
Ir ≠ 0 if r > max {|a|, b}
2
Ir ≠ 0 if r < max {|a|, b}
3
Ir = 0 if r > max {|a|, b} and |a| = b
4
Ir = 0 if |a| < r < b