Are Absolute Harmonicity and Analyticity Related in Functions?

[rasi]

1) If a function is analytic, might its imaginary and real parts be called absolutely harmonic?
2) If real and imaginary parts of a function is not harmonic, then it can't be analytic?

Are these statements true or false? thanks

 

[ShayanJ]

I think using Cauchy-Riemann conditions you can find your answers easily.Just try to get Laplace equation out of them.