Practice Questions for CSIR NET Complex Analysis : Analytic Functions III

Practice Questions for NET JRF Complex Analysis Assignment: Analytic Functions

21. Let u(x,y)=2x(1y) for all real x and y. Then a function v(x,y), so that f(z)=u(x,y)+iv(x,y) is analytic, is






22. Define f:CC by f(z)={0 if Re(z)=0 or Im(z)=0z otherwise  then the set of points where f is analytic is






23. Which of the following is not the real part of an analytic function?






24. The principal value of log(i1/4) is






25. Consider the functions f(z)=x2+iy2 and g(z)=x2+y2+ixy at z=0






26. Consider a function f(z)=u+iv defined on |zi|<1 where u,v are real-valued functions of x,y. If f(z) is analytic then u equals to






27. At z=0, the function f(z)=z2z¯






28. The function sinz is analytic in






29. The function f(z)=|z|2 is






30. An analytic function f(z) is such that Re{f(z)}=2y and f(1+i)=2, then the imaginary part of f(z) is






31. The function f(z)={(z¯)2z2 when z00 when z=0






32. The harmonic conjugate of u(x,y)=x2y2+xy is






33. Let f:CC be given by

f(z)={(z¯)2z when z00 when z=0






34. How many elements does the set {zCz60=1,zk1 for \(0






Post a Comment

0 Comments