EE 204
Lecture 19
Review of Complex Numbers
Complex Numbers:
Any complex number
A
can be expressed as
A
a
jb
=
+
Where:
a
= real part of
A
b
= imaginary part of
A
1
j
≡
−
Both
a
&
b
are
real
numbers
The
bar
on the top is used to denote that
A
is a complex number
Basic Complex Number Operations:
A brief review of basic complex number operations will be presented next
Powers of
j
:
(
)
2
2
1
1
j
=
−
= −
(
)
(
)
(
)
3
2
3
1
1
1
j
j
=
−
=
−
×
−
= −
4
2
2
( 1)
( 1)
1
j
j
j
=
×
= −
× −
=
5
4
(1)
( )
j
j
j
j
j
=
×
=
×
=
6
4
2
(1)
( 1)
1
j
j
j
=
×
=
× −
= −
and so on

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