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

Question

TuteeHUB · Accepted Answer

$\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}$

TuteeHUB · Answer

$\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}$

TuteeHUB · Answer

$\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}$

TuteeHUB · Answer

$\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}$

1.	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
A.	\(\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}\)
B.	\(\frac{{\partial u}}{{\partial x}} = \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}\)
C.	\(\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}\)
D.	\(\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = - \frac{{\partial v}}{{\partial x}}\)
Answer» C. \(\frac{{\partial u}}{{\partial x}} = - \frac{{\partial v}}{{\partial y}}~and~\frac{{\partial u}}{{\partial y}} = \frac{{\partial v}}{{\partial x}}\)

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