Exercise 3.  Represent the following complex numbers in polar form  [Graphics:Images/ComplexGeometryContinuedModHome_gr_164.gif].  

3 (c).  [Graphics:Images/ComplexGeometryContinuedModHome_gr_185.gif].  

Solution 3 (c).

See text and/or instructor's solution manual.

The modulus of  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_186.gif]  is  

        [Graphics:../Images/ComplexGeometryContinuedModHome_gr_187.gif]  

and an argument is  

        [Graphics:../Images/ComplexGeometryContinuedModHome_gr_188.gif].  

Hence, the polar form of  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_189.gif]  is  [Graphics:../Images/ComplexGeometryContinuedModHome_gr_190.gif],  i.e.

        [Graphics:../Images/ComplexGeometryContinuedModHome_gr_191.gif]

We are done.   

Aside.  We can let Mathematica double check our work.

        

[Graphics:../Images/ComplexGeometryContinuedModHome_gr_192.gif]

  

[Graphics:../Images/ComplexGeometryContinuedModHome_gr_193.gif]
[Graphics:../Images/ComplexGeometryContinuedModHome_gr_194.gif]




















This solution is complements of the authors.







































 

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