# Answer to Question #17973 in Complex Analysis for ran

Question #17973

True or False with explanation:-

1.The mean value theorem of a real-valued function of a real variable does not hold in general for complex-valued functions.

2.A real-valued function u in domain D cannot be analytic in D unless it is a constant function.

3.There exists a non-constant real-valued function u in open set D which is analytic in D.

4.A real-valued function u(x,y) is harmonic in D iff u(x,-y) is harmonic in D.

5.If f:D→D’ is analytic and u: D'→R is harmonic then the composition of u & f is harmonic inD.

6.{fn(z)} be a sequence of analytic function in a domain D such that fn→f uniformly inD. Then fn’→f' uniformly in D .

1.The mean value theorem of a real-valued function of a real variable does not hold in general for complex-valued functions.

2.A real-valued function u in domain D cannot be analytic in D unless it is a constant function.

3.There exists a non-constant real-valued function u in open set D which is analytic in D.

4.A real-valued function u(x,y) is harmonic in D iff u(x,-y) is harmonic in D.

5.If f:D→D’ is analytic and u: D'→R is harmonic then the composition of u & f is harmonic inD.

6.{fn(z)} be a sequence of analytic function in a domain D such that fn→f uniformly inD. Then fn’→f' uniformly in D .

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