Project ForgeEngineering Mathematics
Calculus
GATE 2016
Medium
A function f of the complex variable z = x + iy is given as f(x,y) = u(x,y) + i v(x,y), where u(x,y) = 2kxy and v(x,y) = x² - y². The value of k for which the function is analytic is __________.
-1(± 0.1 accepted)
Explanation
Cauchy-Riemann: ∂u/∂x=∂v/∂y → 2ky=-2y → k=-1. Check the other equation: ∂u/∂y=-∂v/∂x → 2kx=-2x → k=-1. Consistent, so k=-1.
Source: GATE ME 2016 Set-2 (2016)
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