GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

© examsiri.com

Question : 44 of 65

Marks: +1, -0

Let

{z}

be a complex variable. For a counter-clockwise integration around a unit circle C, centred at origin,

Φ_{c} \;{1}/{5 z-4} d z=A π i

the value of

A

is

$2 / 5$
$1 / 2$
2
$4 / 5$

Solution:

5 z-4=0

z=\;{4}/{5}

lies inside circle,

|z|=1

∫ \;{1}/{(5 z-4)} d z=A π i

\;{1}/{5} ∫ \;{1}/{(z-\;{4}/{5})} d z=A π i

∫ \;{({1}/{5})}/{(z-\;{4}/{5})} d z=2 π i ⋅ f(\;{4}/{5})=2 π i ×(\;{1}/{5})=\;{2}/{5} π i

A=\;{2}/{5}

© examsiri.com

Go to Question:

Prev Question

Next Question