Section 10.3
The Complex Plane;
De Moivre’s Theorem
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
If z  4  cos 35  i sin 35  and w  2  cos80  i sin 80  find
(a) zw
z
(b)
w
Leave answer in polar form.
(a) zw = 4  cos35  i sin 35  2  cos80  i sin 80 
=  4  2  cos  35  80   i sin  35  80    8cos115  i sin115
z 4  cos 35  i sin 35 
4
(b)
=
= cos  35  80   i sin  35  80  
w 2  cos80  i sin 80 
2
 2 cos  45   i sin  45    2  cos 45  i sin 45 
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Write  2  cos15  i sin15   in standard form a  bi.
4
 2  cos15  i sin15  24  cos  4 15   i sin  4 15  
4
16  cos 60  i sin 60
1
3 
16  
i   8  8 3i
2 2 
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Write  2  2i  in standard form a  bi.
6
First we need 2  2i in polar form.
r  2 2  8  2 2
2
 2  2i 
2
2 
This is in quadrant I.   tan

2 4
1
6
6



 

  2 2  cos  i sin    2 2
4
4 



6

 
  
 cos  6  4   i sin  6  4  





3
3 

 512  cos
 i sin

2
2


Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.