Complex Analysis PU — University of the Punjab
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BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025
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Literary criticism
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this paper consists of 60 marks but now we have 35 marks paper.
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Can you please tell me more past papers please because my exams are starting from next week
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Did you provide the past papers of the science of society uos?
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Paper text
UNIVERSITY OF THE PUNJAB
Q1.
a) Determine the set of points S where the function f(z) = |z - i|'is continuous.
b) Suppose z1 * Z2. Interpret Re(z172) = 0 geometrically in terms of vectors z1 and z2
c) Draw the pair of points z = a + ib and Z = a - ib in the complex plane if
a > 0, b > 0; a >, b < 0; a < 0,b> 0; a, 0,b < 0
(06+06+08)
Q2.
a) Show that the function f(z) = z* is analytic in the domain D = C, and the function
g(z) = |z| is not analytic in any domain.
b) Evaluate
9z2 - iz + 4
- dz
3(22+1).
where the contour is a circle of radius 2, described in the positive direction.
(12+08)
Q3.
a) Show that under the transformation w = sinz, the line × = p, where 2p/n is not an
integer, maps onto a branch of the hyperbola
|w + 1| - |w - 1| = 2 sinp
b) Prove that the expansion of an analytic function in a power series is unique.
(12 +
08)
Q4.
Evaluate
1+x22
× - sinx
*3(23+x2 dx a>0
