Holomorphic harmonic functions confirmation

[cobalt wren]

aren't all holomorphic functions harmonic ?
laplacian (f) = laplacian (u+iv) = uxx + i vxx + uyy + i vyy = (uxx + uyy) + i (vxx + vyy) = 0 + i 0 = 0
since u and v are harmonic functions of f = u + iv which is holomorphic.

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[unreal basalt]

Yes all holomorphic functions are indeed harmonic on the open set where they are holomorphic

Because of the Cauchy-Riemann equations

[cobalt wren]

thanks

[unique grail]

@cobalt wren has given 1 rep to @unreal basalt

[cobalt wren]

+close