Subjects
Applied Mathematics for Electrical Engineering - 3130908
Complex Variables and Partial Differential Equations - 3130005
Engineering Graphics and Design - 3110013
Basic Electronics - 3110016
Mathematics-II - 3110015
Basic Civil Engineering - 3110004
Physics Group - II - 3110018
Basic Electrical Engineering - 3110005
Basic Mechanical Engineering - 3110006
Programming for Problem Solving - 3110003
Physics Group - I - 3110011
Mathematics-I - 3110014
English - 3110002
Environmental Science - 3110007
Software Engineering - 2160701
Data Structure - 2130702
Database Management Systems - 2130703
Operating System - 2140702
Advanced Java - 2160707
Compiler Design - 2170701
Data Mining And Business Intelligence - 2170715
Information And Network Security - 2170709
Mobile Computing And Wireless Communication - 2170710
Theory Of Computation - 2160704
Semester
Semester - 1
Semester - 2
Semester - 3
Semester - 4
Semester - 5
Semester - 6
Semester - 7
Semester - 8
Complex Variables and Partial Differential Equations
(3130005)
CVPDE-3130005
Summer-2020
Question-2c( i )-OR
BE | Semester-
3
Summer-2020
|
27-10-2020
Q2) (c( i ))
4 Marks
Find the fourth roots of -1.
Let,
z
=
-
1
⇒
x
=
-
1
&
y
=
0
θ
π
π
⇒
r
=
1
&
θ
=
π
+
2
kπ
The polar form of complex number,
θ
θ
-
1
=
r
cosθ
+
i
sinθ
π
π
π
π
⇒
-
1
=
1
cos
π
+
2
kπ
+
i
sin
π
+
2
kπ
π
π
π
π
⇒
-
1
1
4
=
cos
π
+
2
kπ
+
i
sin
π
+
2
kπ
1
4
π
π
π
π
⇒
-
1
1
4
=
cos
π
+
2
kπ
4
+
i
sin
π
+
2
kπ
4
(
De
Movire
'
s
Theorem
)
;
k
=
0
,
1
,
2
,
3
.
If
k
=
0
, then
π
π
z
1
=
cos
π
4
+
i
sin
π
4
.
If
k
=
1
, then
π
π
z
2
=
cos
3
π
4
+
i
sin
3
π
4
.
If
k
=
2
, then
π
π
z
3
=
cos
5
π
4
+
i
sin
5
π
4
.
If
k
=
3
, then
π
π
z
4
=
cos
7
π
4
+
i
sin
7
π
4
.
Questions
Go to Question Paper
Q1
(a)
Q1
(b)
Q1
(c ( i ))
Q1
(c ( ii ))
Q2
(a)
Q2
(b)
Q2
(c(i))
Q2
(c(ii))
Q2
(c( i ))
(OR)
Q2
(c ( ii ))
(OR)
Q3
(a)
Q3
(b)
Q3
(c)
Q3
(a)
(OR)
Q3
(b)
(OR)
Q3
(c)
(OR)
Q4
(a)
Q4
(b)
Q4
(c ( i ))
Q4
(c ( ii ))
Q4
(a)
(OR)
Q4
(b)
(OR)
Q4
(c ( i ))
(OR)
Q4
(c ( ii ))
(OR)
Q5
(a)
Q5
(b)
Q5
(c)
Q5
(a)
(OR)
Q5
(b)
(OR)
Q5
(c)
(OR)