Graphics Reference
In-Depth Information
2.4 Addition and Subtraction
Given two complex numbers:
z
1
=
a
+
bi
z
2
=
c
+
di
z
1
±
z
2
=
(
a
±
c
)
+
(
b
±
d
)
i
where the real and imaginary parts are added or subtracted, respectively. For exam-
ple:
z
1
=
+
5
3
i
z
2
=
3
+
2
i
z
1
+
z
2
=
8
+
5
i
z
1
−
z
2
=
2
+
i.
2.5 Multiplication by a Scalar
A scalar is just an ordinary number, and may be used to multiply a complex number
using normal algebraic rules. For example, the complex number
a
+
bi
is multiplied
by the scalar
λ
as follows:
λ (a
+
bi)
=
λa
+
λbi
and a specific example:
2
(
3
+
5
i)
=
6
+
10
i.
2.6 Product of Two Complex Numbers
The product of two complex numbers is evaluated by creating all the terms alge-
braically, and collecting up the real and imaginary terms:
bi
z
2
=
c
+
di
z
1
z
2
=
(a
z
1
=
a
+
+
bi)(c
+
di)
bdi
2
=
ac
+
adi
+
bci
+
=
(ac
−
bd)
+
(ad
+
bc) i
which is another complex number. For example:
