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

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(Complex number)
(Complex number)
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'''Political statement'''
 
'''Political statement'''
  
 +
The professor totally disagrees with the name complex number because, indeed, the construction of '''C''' is much easier than the construction of '''R'''.
 +
 +
From '''Q''' ( set of quotient number) we can also construct a set containing i, which has a square equal to -1, and this construction is considered relatively easy
 +
      Meanwhile,
  
 
== Scan of class note ==
 
== Scan of class note ==

Revision as of 11:39, 21 September 2012

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


Complex number

Definition and properties

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 )

Political statement

The professor totally disagrees with the name complex number because, indeed, the construction of C is much easier than the construction of R.

From Q ( set of quotient number) we can also construct a set containing i, which has a square equal to -1, and this construction is considered relatively easy

     Meanwhile,

Scan of class note

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