GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 27 of 65

Marks: +1, -0

An analytic function

f(z)

of complex variable

z=x+I

y may be written as

f(z)=u(x, y)+i v(x,

, y). Then,

u(x, y)

and

v(x, y)

must satisfy

Solution:

f(z) = u(x, y) + iv(x, y)

is analytic function then it must satisfy the following relations

\;{∂ u}/{∂ x}=\;{∂ v}/{∂ y}

\;{∂ u}/{∂ y}=-\;{∂ v}/{∂ x}

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