Difference between revisions of "12-240/Classnotes for Thursday September 20"

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(Complex number)
(Complex number)
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== Complex number ==
 
== Complex number ==
'''Definition:'''
+
 
  
 
''' C'''={(a,b): a, b <math>\in\!\,</math> '''R'''}
 
''' C'''={(a,b): a, b <math>\in\!\,</math> '''R'''}
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i^2=-1
 
i^2=-1
 +
 +
'''C''' contains '''R''' as {(a,0)}  ( actually, this is not the set of real number but a copy of it )
  
 
[[Image:IMG.jpg]]
 
[[Image:IMG.jpg]]
 
[[Image:IMG2.jpg]]
 
[[Image:IMG2.jpg]]
 
[[Image:IMG3.jpg]]
 
[[Image:IMG3.jpg]]

Revision as of 11:33, 21 September 2012

In this class, the professor completes the lecture about complex number and then introduces vector space.


Complex number

C={(a,b): a, b \in\!\, R}

1 ( of C) = (1,0); 0 ( of C)= (0,0)

i=(0,1)

(a,b)+(c,d)=(a+c,b+d); (a,b)x(c,d)=(ac-bd,ad+bc)

i^2=-1

C contains R as {(a,0)} ( actually, this is not the set of real number but a copy of it )

File:IMG.jpg File:IMG2.jpg File:IMG3.jpg