This preview shows pages 1–3. Sign up to view the full content.
Consistency of Arithmetic Operations on
Complex Numbers in Both
Rectangular and Polar (Exponential) Forms
Consider two complex numbers,
N
1
and
N
2
, written in both
rectangular and polar (exponential) forms:
N
1
=
a
+
j
b
=
a
2
+
b
2
e
j
!
1
where
1
=
tan
–1
(
b
/
a
)
cos
1
( )
=
a
a
2
+
b
2
sin
1
( )
=
b
a
2
+
b
2
N
2
=
c
+
j
d
=
c
2
+
d
2
e
j
2
where
2
=
tan
–1
(
d
/
c
)
cos
2
( )
=
c
c
2
+
d
2
sin
2
( )
=
d
c
2
+
d
2
a
Real
Imag
b
N
1
a
2
+
b
2
1
c
Real
Imag
d
N
2
c
2
+
d
2
2
(0, 0)
(0, 0)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThe rectangular and polar (exponential) forms of complex
numbers shown above are consistent with the Euler relation:
Ae
j
!
=
A
cos
+
jA
sin
A. The rectangular and polar forms of complex numbers yield
identical results when added or subtracted.
Rectangular form
:
N
1
±
N
2
= (
a
+
j
b
)
±
(
c
+
j
d
) = (
a
±
c
) +
j
(
b
±
d
)
Polar (exponential) form
:
N
1
±
N
2
=
a
2
+
b
2
e
j
1
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/17/2008 for the course EECS 202 taught by Professor Plonus during the Spring '08 term at Northwestern.
 Spring '08
 PLONUS

Click to edit the document details