Complex Analysis : Applications of Harmonic Functions

Study concepts, example questions & explanations for Complex Analysis

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Applications Of Harmonic Functions

If  and  are both analytic through a domain , which of the following is true? 

Possible Answers:

None of the other answers

 is nowhere analytic

 must be constant throughout 

 is nowhere differentiable

Correct answer:

 must be constant throughout 


Since  is analytic, the Cauchy-Riemann Equations give us  

Since  is analytic, the Cauchy-Riemann Equations give us .

Putting these two results together gives us 

which implies that  is constant. Similar reasoning gives is that  is constant. This implies that must be constant throughout .

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: