C 20646 (Pages : 2) फिज्ला16.....५०५०००००००००००००००«००«०००००००००००००००

SIXTH SEMESTER U.G. DEGREE EXAMINATION, MARCH 2022
(CBCSS-UG)
Mathematics
MTS 6B 11—COMPLEX ANALYSIS
(2019 Admissions)
Time : Two Hours and a Half Maximum : 80 Marks
Section A

Answer at least ten questions.

Each question carries 3 marks.

All questions can be attended.
Overall Ceiling 30.

Define holomorphic function in a domain D. And give an example for an entire function.
Prove or disprove : if fis differentiable a point z), then fis continuous at that point.
Define harmonic function with example.

Prove that sin2z + cos2z = 1.

State ML inequality.

Define the path independence for a contour integral.

உன்ன ~ ~ ^

State maximum modulus theorem.
a

b
8. Prove that [f(e)at =-[F (jae.
a b

li t ००
9. Prove or disprove if Pa z, =0, then 2 #-1+ 00014712௦6.

10. Find the radius of convergence of 2 ட்‌

11. Define pole of order n. Give an example of a function with simple pole at z = 1.

sinz
12. Find the principal part in the Laurent series expansion about the origin of the function f(z)= प्र
2

Turn over

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