GATE 2016 EC (EC3) – Question 39

Engineering Mathematics · Complex Analysis · 2 marks · Multiple choice

The integral $(2\pi j)^{-1}\oint_c e^z/(z-2)\,dz$ is taken anticlockwise around a closed contour. Its values with z=2 (i) inside and (ii) outside c are respectively

(i) 2.72; (ii) 0
(i) 7.39; (ii) 0
(i) 0; (ii) 2.72
(i) 0; (ii) 7.39

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) (i) 7.39; (ii) 0

Explanation

If z=2 is enclosed once, Cauchy's integral formula gives the normalized integral equal to $e^2=7.389056\ldots$.

If it is outside, the integrand is analytic throughout the enclosed region, so Cauchy's theorem gives zero. The requested pair is therefore **7.39 and 0, B**.

GATE 2016 EC (EC3) – Question 39

Explanation

More Complex Analysis questions