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

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(Complex number)
(Complex number)
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Meanwhile, from '''Q''', the construction of R is extremely hard and hence, of course, much more complicated.
 
Meanwhile, from '''Q''', the construction of R is extremely hard and hence, of course, much more complicated.
  
'''interpretation of complex number'''
+
'''Interpretation of complex number'''
 +
 
 +
Since complex number has two elements, it can be express in geometric form in coordinate plane
  
 
== Scan of class note ==
 
== Scan of class note ==

Revision as of 11:44, 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, from Q, the construction of R is extremely hard and hence, of course, much more complicated.

Interpretation of complex number

Since complex number has two elements, it can be express in geometric form in coordinate plane

Scan of class note

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