Cauchy-Riemann equations

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For $f(z) = u + iv$ to be analytic, one Cauchy–Riemann equation states that:

\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}

\frac{\partial u}{\partial x} = -\frac{\partial v}{\partial y}

\frac{\partial u}{\partial x} = \frac{\partial u}{\partial y}

u = v

If a complex function $f(z) = u + iv$ is analytic, the Cauchy–Riemann equations require $\frac{\partial u}{\partial x} =$ :

\frac{\partial v}{\partial y}

-\frac{\partial v}{\partial y}

\frac{\partial v}{\partial x}

0

The Cauchy–Riemann equations are used to test whether a complex function is:

A.Periodic

B.Analytic (differentiable)

C.Bounded

D.Real-valued

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