A C1100 Pages: 2

Reg No.:_. Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
THIRD SEMESTER B.TECH DEGREE EXAMINATION(S), MAY 2019
Course Code: MA201

Course Name: LINEAR ALGEBRA AND COMPLEX ANALYSIS

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer any two full questions, each carries 15 marks Marks
1 a) Prove that the function sinz is analytic and find its derivative. (7)
b) Under the transformation w = = , find the image of |z—2i| = 2 (8)
2 a) Find the analytic function whose imaginary part is (7)

v(x, 1) = log( x? + y?) + x- 2).

b) Under the transformation w = 22, find the image of the triangular region )8(
bounded by x = 1, y = 1 andx+y = 1.

ಇಟ್ಟ Show that f(z) = വി 00 is not differentiable at z = 0 ^^
0 , 2 = 0
0) Find the bilinear transformation that maps the points —1, i, —1 onto i, 0, —i. (8)
PART छ
Answer any two full questions, each carries 15 marks
4 a) = dz, where C is the 7

Using Cauchy’s integral formula, evaluate J. ತರಾ

circle |2- 1| = 2.
0) Evaluate 1 जगक along (8)

(1) the real axis to 2 and then vertically to 2 + i.
ii) theline2y = x

5 ൮ Find all singular points and residues of the functions (7)

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