Teaching MPPSC Assistant Professor Mock Test Series 2025 Engineering Mathematics Complex Variables Analytic Functions
सम्मिश्र चर z = x + iy के एक वैश्लेषिक फलन f(z) को f (z) = u (x, y) + iv (x, y) के रूप में लिखा जा सकता है। तब u (x, y) और v (x, y) किसे संतुष्ट करेंगे?
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
\(\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}\)