12-240/Classnotes for Thursday September 20: Difference between revisions
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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 |
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 |
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Meanwhile, from '''Q''', the construction of R is extremely hard and hence, of course, much more complicated. |
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Meanwhile, |
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'''interpretation of complex number''' |
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== Scan of class note == |
== Scan of class note == |
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Revision as of 11:41, 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 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
