engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Complex Variables Analytic Functions
The function f(z) of complex variable z = x + iy, where \(i = \sqrt { - 1} ,\) is given as f(z) = e- y sin x + i v(x,y). For this function to be analytic, v(x,y) should be
1
\(-\ e^{-y}\ cosx + \ constant\)
2
\(-\ e^{-y}\ sinx + \ constant\)
3
\(e^{-y}\ cosx + \ constant\)
4
\(e^{-y}\ sinx + \ constant\)