Exercise 4.  Show that  [Graphics:Images/ComplexGeometryContinuedModHome_gr_253.gif],  thus completing the proof of  Theorem 1.3.  

Solution 4.

See text and/or instructor's solution manual.

    For  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_254.gif] and [Graphics:../Images/ComplexGeometryContinuedModHome_gr_255.gif],  let  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_256.gif].  Then  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_257.gif]  for some [Graphics:../Images/ComplexGeometryContinuedModHome_gr_258.gif] and some  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_259.gif].  

Thus,  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_260.gif],  and  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_261.gif].  

This gives  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_262.gif],  so that  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_263.gif].  

Therefore,  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_264.gif].







































 

This solution is complements of the authors.







































 

(c) 2008 John H. Mathews, Russell W. Howell