Graphics Reference
In-Depth Information
+
As an illustration let's find the inverse of 3
4 i
1
4 i) 1
4 i =
( 3
+
3
+
3
4 i
25
=
4
25 i.
Let's test this result by multiplying z by its inverse:
3
25
=
4 i) 3
25 i
4
9
25
12
25 i
12
25 i
16
25 =
( 3
+
25
=
+
+
1
which confirms the correctness of the inverse.
2.10 The Complex Plane
Leonhard Euler (1707-1783) (whose name rhymes with boiler ) played a significant
role in putting complex numbers on the map. His ideas on rotations are also used
in computer graphics to locate objects and virtual cameras in space, as we shall see
later on.
Consider the scenario depicted in Fig. 2.1 . Any number on the number line is
related to the same number with the opposite sign via a rotation of 180°. For exam-
ple, when 2 is rotated 180° about zero, it becomes
2, and when
3 is rotated 180°
about zero it becomes 3.
But as we know that i 2
=−
1 we can write
i 2 n.
n
=
If we now regard i 2
as a rotation through 180°, then i could be a rotation through
90°!
Figure 2.2 shows how complex numbers can be interpreted as 2D coordinates
using the complex plane where the real part is the horizontal coordinate and the
Fig. 2.1 Rotating numbers
through 180° reverses their
sign
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