The GATE Grind

GATE 2025 EE – Question 55

Engineering Mathematics · Complex Variables: Analytic functions, Cauchy integral formula, Taylor series, Laurent series, Residue theorem · 2 marks · Numerical answer

Let $C$ be a clockwise oriented closed curve in the complex plane defined by $|z|=1$. Further, let $f(z)=jz$ be a complex function, where $j=\sqrt{-1}$. Then, $\oint_Cf(z)\,dz=$ ________ (round off to the nearest integer).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0

Explanation

$f(z)=jz$ is analytic everywhere, so by Cauchy's theorem its integral over any closed curve is 0.