harmonic functions

[parsapaki]

if z(r,teta)=u+vi is a complex function and u(r,teta)=a*ln(r) which value of (a) makes (z) a harmonic function ( (a) can be any complex number)?
1) +-1
2) +-i
3) 0
4)all values of (a)

 

[Steven G]

What have you tried? Where are you stuck?
Helpers here are willing to help you solve your problems, but no one here will solve it for you. Please read the posting guidelines.

 

[Steven G]

This is your 2nd post where you failed to show any of your work. I spent time reading your post when I could have been helping another student who follows the posting guidelines. Please read them.

 

[Deleted member 4993]

if z(r,teta)=u+vi is a complex function and u(r,teta)=a*ln(r) which value of (a) makes (z) a harmonic function ( (a) can be any complex number)?
1) +-1
2) +-i
3) 0
4)all values of (a)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[parsapaki]

What have you tried? Where are you stuck?
Helpers here are willing to help you solve your problems, but no one here will solve it for you. Please read the posting guidelines.

What have you tried? Where are you stuck?
Helpers here are willing to help you solve your problems, but no one here will solve it for you. Please read the posting guidelines.

hi , This is a question from an exam that has already been held and I want to know which option is correct. I consider option 1 to be correct

 

[Deleted member 4993]

hi , This is a question from an exam that has already been held and I want to know which option is correct. I consider option 1 to be correct

What is your reasoning behind your choice?

 

[parsapaki]

What is your reasoning behind your choice?

I wrote the Laplace equation for the function in question, and option one seemed to be the most logical answer (according to the main branch of [math]ln[/math]), although option four also arouses my skepticism .If option four is correct, then zero is also known as the correct answer, while according to the main branch of the logarithm, answers greater than zero are acceptable. so I do not know that my solution is correct or I have a mistake in my Logical analysis

 

[Eugenio]

All values of [imath]a[/imath] mean that [imath]1+i, -i, 2i, 3+\sqrt{2}i, e^{-i}, 0, etc[/imath] are acceptable. The answers above are saying that only those are acceptable.