A 08000MA201122004 Pages: 2

Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
Third Semester B.Tech Degree (S,FE) Examination January 2022 (2015 Scheme)

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) Define continuity of a complex valued function f(z) at a point 2 = zo, Also check whether (7)

Im(z?)
the function f(z) = परमं *0
0 z=0

b) Check whether U(x,y) = x? - 30” + 357 - 37 + 1 is harmonic .If so find its harmonic (8)

is continuous at 7 = 0.

conjugate.

2 a) Show that if f(z) = u+iv is an analytic function with constant modulus, then f is a constant. (8)
0) Write the real and imaginary parts of the transformation f(z) = =~ Also find the image of (7)
|2|< 1 under this transformation.

3 a) 9) Find the image of the circle x* + y? — 6 = 0 under the transformation w = ⋅ (7)

ii) Find the image of the strip 1< y < 2 under the transformation w = sinz
b) Find the bilinear transformation which maps (-1, -i, 0) to (0, -i, 2). Also find the critical (8)
points of this transformation.
PART छ
Answer any two full questions, each carries 15 marks
4 9) Evaluate fo" Zaz along (8)
a) the line x = 3)

b) along 2(t)=3ttit?

0) Using Cauchy’s integral formula Evaluate the integral || ಕ ‏ہے‎ dz over the circle |z|=1. (7)

5 2) Find the singular points and residue at singular point of the function f(z) = ‏ہس‎ which lie (7)
inside the circle || = 3/2.

0) Find the Laurent series of f(z) = 211 valid in the region 2 > |2| < 5 around 2 = 0۰ (8)

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