can any1 explain some small stuff about harmonic and conjugate functions?

Question

anonymous · Answer

i know that for a function to be harmonic it must satisfy the laplace equation in 2 dimension, and a conjugate function must satisfy the cauchy riemanns equation.
so all conjugate must be harmonic also? or vice versa, or i cant make that relationship?

anonymous · Answer

In mathematics, a function  defined on some open domain  is said to have as a conjugate a function  if and only if they are respectively real and imaginary part of a holomorphic function  of the complex variable  That is,  is conjugate to  if  is holomorphic on  As a first consequence of the definition, they are both harmonic real-valued functions on . Moreover, the conjugate of  if it exists, is unique up to an additive constant. Also,  is conjugate to  if and only if  is conjugate to .

anonymous · Answer

so a conjugate function is always harmonic, ie. called a conjugate harmonic function?
since conjugate function need to satisfy the CR equation, and by the 2nd CR equation it satisfies the laplace equation. so can i conclude like this?