高等考試 107年 [電力工程] 工程數學

第 14 題

複變函數 $f(x+iy) = u(x, y) + iv(x, y)$ 在 $x+iy$ 為可微分，則下列何條件必須滿足？

A $\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$ 和 $\frac{\partial v}{\partial x} = \frac{\partial u}{\partial y}$
B $\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$ 和 $\frac{\partial v}{\partial x} = -\frac{\partial u}{\partial y}$
C $\frac{\partial u}{\partial x} = -\frac{\partial v}{\partial y}$ 和 $\frac{\partial v}{\partial x} = \frac{\partial u}{\partial y}$
D $\frac{\partial u}{\partial x} = -\frac{\partial v}{\partial y}$ 和 $\frac{\partial v}{\partial x} = -\frac{\partial u}{\partial y}$

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