Complex Number Complex number :
a + bi
real
Y ↑
① Introduction
5
3, 4
E
,
- 5
real
imaginary
0 519
.
-
I =
(a , b)
When i = F
ex) F8 5 F 5i
[3)
= · =
Recall Vector 31 + 4j =
x3 2x5 =
do need to learn complex number ?
Why we
-
-
What are the applications of complex number ?
1 . for
modelling periodic motions
(water/lightwaves
convenient for functions
.
2 It is a
language expressing wave
. To
3 provide a natural and short proof for the fundamental theorem
of
algebra which states that the field of complex numbers is
algebraically closed
.
Electrical & Electronic
Used
by Engineers to define the
4.
Alternating
Current (AC) concept of Impedance
I
x + 1 = 0 x = + F
x = -
19 =
Ii
, )i
② i = i is =
i 12 -
i =
1 =
F i' =-
let
-
i =
i i i =
- 26
-
= -
1 .
i =
1 = -
1 . -
1 18 =
1 j125 =
u =
i =
i
12
③ Equivalence -
If x +
ye = a+ bi then x= ad b(X, y) =
(a b)
y
=
, ,
④ Addition/Subtraction
(a + bi) + (c + di) =
(a + c) + (b + d)i
(a + bi) -
( + di) = (a -
x) + (b -
d)i
Ex) 2
,
=
(2 ,
-
5) find 2
,
+
z = (0 -4)
,
2
= ( 2
-
,
1) 2. - 2
z
=
(4
,
-
6)
⑤ Scalar multiplication
-
k(a bi) + =
ka kbi +
ex) -
4(5 + 3i) = -
20 -
12e
a + bi
real
Y ↑
① Introduction
5
3, 4
E
,
- 5
real
imaginary
0 519
.
-
I =
(a , b)
When i = F
ex) F8 5 F 5i
[3)
= · =
Recall Vector 31 + 4j =
x3 2x5 =
do need to learn complex number ?
Why we
-
-
What are the applications of complex number ?
1 . for
modelling periodic motions
(water/lightwaves
convenient for functions
.
2 It is a
language expressing wave
. To
3 provide a natural and short proof for the fundamental theorem
of
algebra which states that the field of complex numbers is
algebraically closed
.
Electrical & Electronic
Used
by Engineers to define the
4.
Alternating
Current (AC) concept of Impedance
I
x + 1 = 0 x = + F
x = -
19 =
Ii
, )i
② i = i is =
i 12 -
i =
1 =
F i' =-
let
-
i =
i i i =
- 26
-
= -
1 .
i =
1 = -
1 . -
1 18 =
1 j125 =
u =
i =
i
12
③ Equivalence -
If x +
ye = a+ bi then x= ad b(X, y) =
(a b)
y
=
, ,
④ Addition/Subtraction
(a + bi) + (c + di) =
(a + c) + (b + d)i
(a + bi) -
( + di) = (a -
x) + (b -
d)i
Ex) 2
,
=
(2 ,
-
5) find 2
,
+
z = (0 -4)
,
2
= ( 2
-
,
1) 2. - 2
z
=
(4
,
-
6)
⑤ Scalar multiplication
-
k(a bi) + =
ka kbi +
ex) -
4(5 + 3i) = -
20 -
12e
