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GATE2020-ME-2: 27
The function $f(z)$ of complex variable $z=x+iy$, where $i=\sqrt{-1}$, is given as $f(z)=(x^3-3xy^2)+i \: v(x,y)$. For this function to be analytic, $v(x,y)$ should be $(3xy^2-y^3) +$ constant $(3x^2y^2-y^3) +$ constant $(x^3-3x^2 y) +$ constant $(3x^2y-y^3) +$ constant

go_editor asked in Calculus Sep 18, 2020

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GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).

go_editor asked in Calculus Feb 19, 2020

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GATE2019 ME-2: 4
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ ...

Arjun asked in Calculus Feb 9, 2019

by Arjun

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