Example
1.10. If
, then
and
.
It would be a mistake to use
as an acceptable value for
,
as the point z associated with
and
is in the first quadrant, whereas
is in the third quadrant. A correct choice for
is
. Thus
, and
,
where n is any integer. In
this case,
, and
.
Explore Solution 1.10.
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_83.gif]](../Images/ComplexGeometryContinuedMod_gr_83.gif)
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_84.gif]](../Images/ComplexGeometryContinuedMod_gr_84.gif)
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_85.gif]](../Images/ComplexGeometryContinuedMod_gr_85.gif)
Here is another way to look at it.
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_86.gif]](../Images/ComplexGeometryContinuedMod_gr_86.gif)
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_87.gif]](../Images/ComplexGeometryContinuedMod_gr_87.gif)
(c) 2006 John H. Mathews, Russell W. Howell