Graphics Reference
In-Depth Information
2.13.1 Summary of Complex Operations
Complex number
where
i
2
z
=
a
+
bi
=−
1
.
Addition and subtraction
z
1
=
a
+
bi
z
2
=
c
+
di
z
1
±
z
2
=
(a
±
c)
+
(b
±
d) i.
Scalar product
λz
=
λa
+
λbi.
Modulus
a
2
b
2
.
|
z
|=
+
Product
z
1
z
2
=
(ac
−
bd)
+
(ad
+
bc) i.
Complex conjugate
z
∗
=
−
a
bi.
Division
ac
bc
i.
z
1
z
2
=
+
bd
−
ad
+
c
2
d
2
c
2
d
2
+
+
Inverse
z
∗
z
−
1
=
2
.
|
z
|
Polar form
z
=
r (
cos
θ
+
i
sin
θ)
r
=|
z
|
θ
=
arg
(z)
re
iθ
.
z
=
Rotors
R
θ
=
cos
θ
+
i
sin
θ
R
†
θ
=
cos
θ
−
i
sin
θ.
