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*Re( d/dz f(z,z_)) and curl f(x,y) = 2*Im( d/dz f(z,z_

*)), where f(z,z_*) is just f(x,y) expressed in z and z conjugate (z_

*). Is there any way of proving the fundamental properties of div and curl and/or understanding them better by looking at d/dz f(z,z_*)?