This module is part of the collection, A First Course in Electrical and Computer Engineering. The LaTeX source files for this collection were created using an optical character recognition technology, and because of this process there may be more errors than usual. Please contact us if you discover any errors.
e
j
θ
=
lim
n
→
∞
(
1
+
j
θ
n
)
n
=
∑
n
=
0
∞
1
n
!
(
j
θ
)
n
=
cos
θ
+
j
sin
θ
cos
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
)
!
θ
2
n
;
sin
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
!
θ
2
n
+
1
e
j
θ
=
lim
n
→
∞
(
1
+
j
θ
n
)
n
=
∑
n
=
0
∞
1
n
!
(
j
θ
)
n
=
cos
θ
+
j
sin
θ
cos
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
)
!
θ
2
n
;
sin
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
!
θ
2
n
+
1
cos
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
)
!
θ
2
n
;
sin
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
!
θ
2
n
+
1
cos
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
)
!
θ
2
n
;
sin
θ
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
!
θ
2
n
+
1
sin
2
θ
+
cos
2
θ
=
1
sin
2
θ
+
cos
2
θ
=
1
(1)
sin
(
θ
+
φ
)
=
sin
θ
cos
φ
+
cos
θ
sin
φ
sin
(
θ
+
φ
)
=
sin
θ
cos
φ
+
cos
θ
sinφ(2)
cos
(
θ
+
φ
)
=
cos
θ
cos
φ
-
sin
θ
sin
φ
cos
(
θ
+
φ
)
=
cos
θ
cos
φ
-
sinθsinφ(3)
sin
(
θ
-
φ
)
=
sin
θ
cos
φ
-
cos
θ
sin
φ
sin
(
θ
-
φ
)
=
sin
θ
cos
φ
-
cosθsinφ(4)
cos
(
θ
-
φ
)
=
cos
θ
cos
φ+sinθsin
φ
cos
(
θ
-
φ
)
=
cos
θ
cosφ+sinθsinφ(5)
ejθ=cosθ+jsin
θ
ejθ=cosθ+jsinθ(6)
sin
θ
=
e
j
θ
-
e
-
j
θ
2
j
sin
θ
=
e
j
θ
-
e
-
j
θ
2
j
(7)
cosθ=ejθ+e-jθ2cosθ=ejθ+e-jθ2(8)
(cosθ+jsinθ)n=cosnθ+jsinnθ(cosθ+jsinθ)n=cosnθ+jsinnθ(9)
(
x
+
y
)
N
=
∑
n
=
0
N
N
n
x
n
y
N
-
n
;
N
n
=
N
!
(
N
-
n
)
!
n
!
(
x
+
y
)
N
=
∑
n
=
0
N
N
n
x
n
y
N
-
n
;
N
n
=
N
!
(
N
-
n
)
!
n
!
(10)
2
N
=
∑
n
=
0
N
N
n
2
N
=
∑
n
=
0
N
N
n
(11)
∑
k
=
0
∞
a
z
k
=
a
1
-
z
|
z
|
<
1
∑
k
=
0
∞
a
z
k
=
a
1
-
z
|
z
|
<
1
(12)
∑
k
=
0
N
-
1
a
z
k
=
a
(
1
-
z
N
)
1
-
z
z
≠
1
∑
k
=
0
N
-
1
a
z
k
=
a
(
1
-
z
N
)
1
-
z
z
≠
1
(13)
f
(
x
)
=
∑
k
=
0
∞
f
(
k
)
(
a
)
(
x
-
a
)
k
k
!
f
(
x
)
=
∑
k
=
0
∞
f
(
k
)
(
a
)
(
x
-
a
)
k
k
!
(14)
(
Maclaurin's Series if
a
=
0
)
(
Maclaurin's Series if
a
=
0
)
(15)
(What does "Endorsed by" mean?)
"Reviewer's Comments: 'I recommend this book as a "required primary textbook." This text attempts to lower the barriers for students that take courses such as Principles of Electrical Engineering, […]"