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MA243 Final Exam - Complex Analysis
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MCQs on Complex Analysis.

MA243 Final Exam - Complex Analysis
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25 Questions

1. Consider the set
given by
. Which of the following is true?
2. Let
, with
, where
and
are real-valued. Let
denote the ball of radius
centered at
. Which of the following is true?
3. Let
denote the punctured unit disk:
. Which of the following is false?
4. Let
be the Moebius transformation such that
,
, and
. What is
?
5. If
satisfies
, writing
, which of the following statements holds?
6. Consider the function
. Denote the punctured unit disc by
. Let
and
. Which of the following statements is false?
7. Which of the following is true?
8. Suppose
is a function on an open set
. Let
be a piecewise smooth, simple curve in
Let
be a smooth parametrization of
. Which of the following is true?
9. Let
be given by
. Let
. Then which of the following is true?
10. The proof that holomorphic functions on open, connected sets have power series representations relies on which of the following results?
11. Let
be a simply connected, open set. Let
be an entire function, and let
on
. Which of the following is the strongest statement that can be made about
?
12. Which of the following pairs of functions fails to satisfy the Cauchy-Riemann equations?
13. Which of the following smooth curves in the complex plane is longest?
14. Let
. Let
be an accumulation point of
, and let
be a complex number. Choose the correct definition for the following statement:
15. Let
be a map which is conformal from
to
, where
. Which of the following is a possible choice for
?
16. Let
be the principle value of the logarithm. Which of the following could be the preimage of the set
?
17. Let
. Define a mapping on
by
. What is
?
18. Which of the following is true of the complex-valued function
?
19. Consider the power series
. Which of the following is false?
20. Suppose that
is a simply connected, open set. Let
be a nonconstant function. Which of the following is true?
21. Let
and
be non-constant holomorphic functions on
with
. Let
be a bounded domain. Which of the following is possible?
22. Define the following contours:


for
.

for
.

for
.
Which of the following is true?
23. Let
. Let
. Let
. Which of the following is false?
24. Let
be a function which is analytic on a domain
, and let
be a simple contour in
. Which of the following is true?
25. Let
. If
, what is
?

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