12-240/Classnotes for Thursday September 20 - Revision history

Zetalda at 02:54, 28 September 2012

2012-09-28T02:54:49Z

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 Image:12-240-0920-2.jpg|Page 2
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 </gallery>

2012-09-27T10:44:30Z

Scan of class note

← Older revision		Revision as of 06:44, 27 September 2012
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	Moreover, complex number can be expressed in polar coordinates:		Moreover, complex number can be expressed in polar coordinates:

	== Scan of class note ==


	[[Image:IMG.jpg]]
	[[Image:IMG2.jpg]]
	[[Image:IMG3.jpg]]

	== Lecture 4, scanned notes upload by [[User:Starash\|Starash]] ==		== Lecture 4, scanned notes upload by [[User:Starash\|Starash]] ==

2012-09-22T22:30:16Z

Complex number

← Older revision		Revision as of 18:30, 22 September 2012
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	'''Interpretation of complex number'''		'''Interpretation of complex number'''

	Since complex number has two elements, it can be express in geometric form in coordinate plane		Since complex number has two real number elements, it can be express in geometric form in coordinate plane, in this case, called complex plane.

			Consider two complex numbers: A=a1 + b1i, B= a2 + b2i.

			In complex plane they are expressed in the form of two points A (a1, b1), B(a2, b2)

			Note that the y axis and x axis in ordinary coordinate plane will become Img axis and Real axis respectively in complex plane.

			The point C (a1 + a2, b1 + b2) is the expression of the sum of A and B in complex plane.

			Moreover, complex number can be expressed in polar coordinates:

	== Scan of class note ==		== Scan of class note ==

2012-09-22T18:52:23Z

← Older revision		Revision as of 14:52, 22 September 2012
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			{{12-240/Navigation}}
	In this class, the professor completes the lecture about complex number and then introduces vector space.		In this class, the professor completes the lecture about complex number and then introduces vector space.


	== Complex number ==		== Complex number ==

2012-09-22T00:39:15Z

← Older revision		Revision as of 20:39, 21 September 2012
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	[[Image:IMG2.jpg]]		[[Image:IMG2.jpg]]
	[[Image:IMG3.jpg]]		[[Image:IMG3.jpg]]

			== Lecture 4, scanned notes upload by [[User:Starash\|Starash]] ==

			<gallery>
			Image:12-240-0920-1.jpg\|Page 1
			Image:12-240-0920-2.jpg\|Page 2
			Image:12-240-0920-3.jpg\|Page 3
			</gallery>

2012-09-21T16:44:01Z

Complex number

← Older revision		Revision as of 12:44, 21 September 2012
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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 ==

2012-09-21T16:42:09Z

Complex number

← Older revision		Revision as of 12:42, 21 September 2012
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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
	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'''

2012-09-21T16:41:50Z

Complex number

← Older revision		Revision as of 12:41, 21 September 2012
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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
			Meanwhile, from '''Q''', the construction of R is extremely hard and hence, of course, much more complicated.
	Meanwhile,

			'''interpretation of complex number'''

	== Scan of class note ==		== Scan of class note ==

2012-09-21T16:39:56Z

Complex number

← Older revision		Revision as of 12:39, 21 September 2012
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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 ==

2012-09-21T16:34:51Z

Complex number

← Older revision		Revision as of 12:34, 21 September 2012
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	== Complex number ==		== Complex number ==

			'''Definition and properties'''

	''' C'''={(a,b): a, b <math>\in\!\,</math> '''R'''}		''' C'''={(a,b): a, b <math>\in\!\,</math> '''R'''}
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	'''C''' contains '''R''' as {(a,0)} ( actually, this is not the set of real number but a copy of it )		'''C''' contains '''R''' as {(a,0)} ( actually, this is not the set of real number but a copy of it )

			'''Political statement'''


			== Scan of class note ==


	[[Image:IMG.jpg]]		[[Image:IMG.jpg]]