Question

If a function satisfies laplace equation, prove it is analytic

Answer 1

∂2u∂x2+∂2u∂y2=0,∂2v∂x2+∂2v∂y2=0∂2u∂x2+∂2u∂y2=0,∂2v∂x2+∂2v∂y2=0

from

∂u∂x=∂v∂y,∂u∂y=−∂v∂x