Basic Definitions and Graphical Representation of Complex Numbers Concepts 1
Definition 1
.
A complex number,
z,
is a number of the form
z = x+iy
where x and y
are real numbers and
.
Note:
i2
= -1.
Definition 2
.
For the complex number
z=x+iy,
the real numbers
x
and
y
are known as the
real
and
imaginary
parts of
z
, respectively, and denoted
Re z=x,
Im z=y.
Definition 3
.
Two complex numbers
z1=x1+iy1
and
z2 = x2+iy2
are defined to be equal if and only if their real parts are equal and their imaginary parts are
equal; that is,
z1
=z2
if and only if
x1=
x2
and
y1=
y2.
Consequence. If the complex number
x+iy=0, then
x=0
and
y=0.
Definition 4
.
Let z=x+iy. Then the complex conjugate of
z, denoted
,
is defined as
=x-iy.