Let f be a non-constant entire function such that |f(z)| = 1 for |z| = 1.
Let U denote the open unit disk around 0.
Which of the following is FALSE ?
f(z) is a non-constant entire functionsuch that
|f(z)| = 1 for |z| = 1.U = {z ∈ C | |z| < 1}
According to the given condition f(z) will look like:f(z) = ; ∀z ∈ C .
Stepwise Analysis:
• Option (A) : As f(c) = c True.
• Option (B) : f(z) = 0 ==> z = 0 , so f has at least one zero in U True.
• Options (C) and (D) : clearly f can have at most finitely many distinctzeros in C,
but f(z) cannot have a zero outside USo, Statement (D) is false
==> Option (D) is correct.
If ,
Which of the following statements is necessarily true ?
Let Y={1,2,3,…,100} and let h:Y→Y be a strictly increasing function. The total number of functions g:Y→Y satisfying g(h(j))=h(g(j)) for all j∈Y are ?
Let f be a holomorphic function on the disc
Assume that the only zero of f in the closed unit disc
is a simple zero at the origin. Let be the positively oriented circle
The integral equals ?
Sum of the infinite series
is equal to ?
A function f: ℂ → ℂ is said to be analytic at ∞, if the function g defined by
g(w) = f () is analytic at 0 with an appropriate value given for g(0).
Which of the following statements is true?
Let p be a positive integer. Consider theclosed curve .
Let f be afunction holomorphic in whereR >1. If f has a zero only at ,and it is of multiplicity q , then equals?
Let
Which of the following is FALSE ?
If | | = 1 for a complex number z = x + iy, x, y ∈ R,then.
which of thefollowing is true ?
Let f be a non-constant entire function such that |f(z)| = 1 for |z| = 1.
Let U denote the open unit disk around 0.
Which of the following is FALSE ?
