Example 1.12. In example 1.10 we investigated the polar form of , and saw that and . Now we have .
Explore Solution 1.12.
(c) 2006 John H. Mathews, Russell W. Howell
![[Graphics:Images/ComplexGeometryContinuedMod_gr_142.gif]](../Images/ComplexGeometryContinuedMod_gr_142.gif){kind=small}
, and
saw that ![[Graphics:Images/ComplexGeometryContinuedMod_gr_143.gif]](../Images/ComplexGeometryContinuedMod_gr_143.gif){kind=small}
and ![[Graphics:Images/ComplexGeometryContinuedMod_gr_144.gif]](../Images/ComplexGeometryContinuedMod_gr_144.gif){kind=small}
. Now
we have![[Graphics:Images/ComplexGeometryContinuedMod_gr_145.gif]](../Images/ComplexGeometryContinuedMod_gr_145.gif){kind=small}
. , and
saw that and . Now
we have. ![[Graphics:../Images/ComplexGeometryContinuedMod_gr_146.gif]](../Images/ComplexGeometryContinuedMod_gr_146.gif)
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_147.gif]](../Images/ComplexGeometryContinuedMod_gr_147.gif)
![[Graphics:../Images/ComplexGeometryContinuedMod_gr_148.gif]](../Images/ComplexGeometryContinuedMod_gr_148.gif)