(Defination)
(Properties)
 
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== Review of Complex Number ==
 
== Review of Complex Number ==
  
  
== Defination==
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== Definition==
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<pre>
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    Complex number is the combination of real number and imaginary number. It's basic form is a+bi, Where
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a is the real part and bi is the imaginary part.
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    i is the unit for imaginary number. In a complex coordinate, a+bi is point(a,b). The distance between
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this point and the origin is the square root of (a^2 + b^2).
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    In the form a+bi, when b=0, the complex number belongs to real number; when a=0, the complex number
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belongs to imaginary number; when they both are not zero, it belongs to complex region.
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    The triangular form of a complex number is Z=r(cosx + isinx). r is the distance between point Z and
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the origin on a complex coordiante. rcosx is real part and irsinx is the imaginary part.
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</pre>
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    Imaginary number comes to use when people want to refer to a number which could not be represented by any real number,
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== Properties ==
such as the square root of a negative number. When we combine a real number and an imaginary number together, we get a  
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:* Addition: <math>\,(a + bi) + (c + di) = (a + c) + (b + d)i</math>
complex number.
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:* Subtraction: <math>\,(a + bi) - (c + di) = (a - c) + (b - d)i</math>
   
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:* Multiplication: <math>\,(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad)i</math>
== Imaginary Number ==
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:* Division: <math>\,\frac{(a + bi)}{(c + di)} = \left({ac + bd \over c^2 + d^2}\right) + \left( {bc - ad \over c^2 + d^2} \right)i\,,</math>
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where ''c'' and ''d'' are not both zero.
  
  We use i to represent <math>sqrt(-1)</math>.
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**Source for wikipedia: [[http://en.wikipedia.org/w/index.php?title=Complex_number&action=edit&section=4]]

Latest revision as of 16:26, 2 September 2008

Review of Complex Number

Definition

    Complex number is the combination of real number and imaginary number. It's basic form is a+bi, Where
a is the real part and bi is the imaginary part. 

    i is the unit for imaginary number. In a complex coordinate, a+bi is point(a,b). The distance between 
this point and the origin is the square root of (a^2 + b^2).

    In the form a+bi, when b=0, the complex number belongs to real number; when a=0, the complex number 
belongs to imaginary number; when they both are not zero, it belongs to complex region.

    The triangular form of a complex number is Z=r(cosx + isinx). r is the distance between point Z and 
the origin on a complex coordiante. rcosx is real part and irsinx is the imaginary part.


Properties

  • Addition: $ \,(a + bi) + (c + di) = (a + c) + (b + d)i $
  • Subtraction: $ \,(a + bi) - (c + di) = (a - c) + (b - d)i $
  • Multiplication: $ \,(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad)i $
  • Division: $ \,\frac{(a + bi)}{(c + di)} = \left({ac + bd \over c^2 + d^2}\right) + \left( {bc - ad \over c^2 + d^2} \right)i\,, $

where c and d are not both zero.

    • Source for wikipedia: [[1]]

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood