Any complex numbercan be written in the form
where
and
if
if
if
if
is called the argument of the complex number z and may be written
It is actually the angle taken clokwise from the positive real axis to the line drawn from the origin to the point z. The argument of a complex number has the property that it can increase by any multiple of
and still return the same complex number, since each increase in the argument by
rotates the complex number once about the origin and returns it to the same point.
We can define the argument of a point relative to any point in the complex plane. Relative to the pointthe argument of
is writen
and is the angle between the line from
to
and a line drawn from
in the direction of the positive real axis.