Graphics Reference
In-Depth Information
Fig. 2.2
The graphical representation of complex numbers
imaginary part is the vertical coordinate. The figure also shows four complex num-
bers:
p
=
1
+
2
i,
q
=−
2
+
i,
r
=−
1
−
2
i,
s
=
2
−
i
which happen to be 90° apart. For example, the complex number
p
in Fig.
2.2
is
rotated 90° to
q
by multiplying it by
i
:
2
i
2
i (
1
+
2
i)
=
i
+
=−
2
+
i.
The point
q
is rotated another 90° to
r
by multiplying it by
i
:
i
2
i (
−
2
+
i)
=−
2
i
+
=−
−
1
2
i.
The point
r
is rotated another 90° to
s
by multiplying it by
i
:
2
i
2
i (
−
1
−
2
i)
=−
i
−
=
2
−
i.
Finally, the point
s
is rotated 90° back to
p
by multiplying it by
i
:
2
i
−
i
2
i (
2
−
i)
=
=
1
+
2
i.
2.11 Polar Representation
The complex plane provides a simple mechanism to represent complex numbers
graphically. This in turn makes it possible to use a
polar representation
as shown
