Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Complex Variables Analytic Functions
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) must satisfy
1
\(\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}\)
2
\(\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}\)
3
\(\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}\)
4
\(\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}\)