Kingdom of Saudi Arabia
Ministry of Higher Education
Salman Bin Abdul Aziz University
College of Science & Humanity Studies
Mathematics Department
Course Symbol: Math4350
Time: 1:00 hours
Course Name: Complex analysis
Date: 25 / 2/ 1436
Total Marks: 15 Marks
Second Exam (1st Semester) 1434/1435
Question (1)
(5 Marks)
Choose the correct answer:1- Let = , + (, ) Then () is differentiable and (଴ ) = __________
a. ௜ఏ (௥ + ௥ )
b. ି௜ఏ (௥ + ௥ )
c. ௜ఏ (ఏ + ௥ )
d. ି௜ఏ (ఏ + ௥ )
2- The principal value of (−)௜ is __________
a. −
b. c. 2
d. గ
ଶ
గ
ସ
3- Let ௭ = −2, then z = _________ where (n = 0, ±1, ±2, ±3, … … … . . )
ଵ
a. ln 2 + (2 + 2)
b. ln 2 + (2 + )
c. ln 2 + (2 + 1)
d. ln 2 + 2
4- + = ___________
ଷ
a. −
c. b. ଵ
d. −
௭
ଵ
௭
5- log(1 − ) = ___________
గ
a. ln 2 − b.
ସ
ଵ
గ
ଶ
ସ
ଵ
ଶ
గ
ln 2 − ଶ
గ
c. ln 2 − d. ln 2 − ଶ
Question(2)
(4 Marks)
Suppose that:
= , + (, , ଴ = ଴ + ଴ and ଴ = ଴ + ଴
Prove that: lim௭→௭బ = ଴ if and only if
limሺ௫,௬ሻ→(௫బ,௬బ) , = ଴
Question(3)
and
limሺ௫,௬ሻ→(௫బ,௬బ) , = ଴
(5 Marks)
Show that the function = sin cosh + 2 cos sinh + ଶ − ଶ + 4 is
a harmonic and determine the corresponding analytic function = + .

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