All Complex Analysis Resources
Example Questions
Example Question #51 : Complex Analysis
If and are both analytic through a domain , which of the following is true?
Possible Answers:
must be constant throughout
is nowhere differentiable
None of the other answers
is nowhere analytic
Correct answer:
must be constant throughout
Explanation:
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 .
All Complex Analysis Resources
Popular Subjects
ACT Tutors in Atlanta, Biology Tutors in New York City, Reading Tutors in Denver, Algebra Tutors in Denver, ISEE Tutors in Dallas Fort Worth, ISEE Tutors in Washington DC, LSAT Tutors in Philadelphia, SSAT Tutors in New York City, Calculus Tutors in Phoenix, Computer Science Tutors in Miami
Popular Courses & Classes
LSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Los Angeles, GMAT Courses & Classes in Denver, GMAT Courses & Classes in San Diego, Spanish Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Boston, ISEE Courses & Classes in Denver, ACT Courses & Classes in Phoenix, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Dallas Fort Worth
Popular Test Prep
GRE Test Prep in Miami, SAT Test Prep in Phoenix, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Seattle, GRE Test Prep in Seattle, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Washington DC, MCAT Test Prep in Miami, SSAT Test Prep in Denver, LSAT Test Prep in Seattle