CauchyRiemanni
The Cauchy-Riemann equations are a pair of differential equations that are fundamental in complex analysis. They provide a necessary and sufficient condition for a complex function to be differentiable. A complex function $f(z) = u(x, y) + iv(x, y)$, where $z = x + iy$, $u(x, y)$ is the real part, and $v(x, y)$ is the imaginary part, is said to be complex differentiable at a point $z_0$ if the limit $\lim_{h \to 0} \frac{f(z_0 + h) - f(z_0)}{h}$ exists.
The Cauchy-Riemann equations are expressed as: $\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$ and $\frac{\partial u}{\partial y}
These equations are crucial because they connect the concept of differentiability of a complex function to
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