Hamdard University – Islamabad Campus
Hamdard Institute of Engineering & Technology
Department of Electrical Engineering
Course Title: Complex Variables and Transforms
Exam: Mid-Term Exam
Maximum Marks: 30
Course Instructor: Engr. M. Najeeb
Semester: Fall 2020
Date:
4th Jan, 2021
Time: 12 PM to 12 AM
Important Instructions:



Attempt all questions.
Students will solve all the questions on white paper and submit the answer sheet in
PDF format on eLMS and also email it on m.najeeb@hamdard.edu and
helpdesk.exam@hamdard.edu
Your PDF size should not exceed 2MB. If size is large, break it into parts (maximum 3
files each having size less than 2MB) and upload all files.
(CLO_1), (Cognitive Level C2, i.e., Understanding), (PLO_1, i.e., Engineering Knowledge)
Question 1
a) Let
, calculate
in the form
, also express z in
polar form.
(4)
b) Calculate the solution of given equation and also graph the solutions. Here z is a complex
variable.
(5)
(CLO_2), (Cognitive Level C2, i.e., Understanding), (PLO_2, i.e., Problem Analysis)
Question 2
a) Calculate the continuity of the given complex variable function
and for
the function f is equal to
b) Let
at
.
be a complex function calculate its derivative at
, if
(4)
. (4)
c) Show whether the following complex function is harmonic or not? If harmonic than
calculate its conjugate.
(5)
Page 1 of 2
d) Describe whether the following complex function is Analytic or not.
(3)
e) Calculate the solution of following equation.
(5)
Page 2 of 2