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Why the point of x + iy would be (x, y) ?

  1. Sep 22, 2009 #1
    What argand diagrams really are ? Is there any differance between graph and argand diagram?

    For complex number i is a sign that is count as [tex]\sqrt[]{-1}[/tex]
    Then why the point for a + ib would be (a, b) in argand diagram ?

    That means, x = real part = a
    y = imaginary part = b
    so if i want to find out real numbers point than it would be on x axis alone, right? [would the point for 'a' (a € Real number) would be (a, 0) in argand diagram ?]
     
  2. jcsd
  3. Sep 22, 2009 #2
    I just think of it as a matter of notation. To develop the ordered pairs of real numbers, define an addition and multiplication on R^2:

    (a,b) + (x,y) = (a+x, b+y)
    (a,b) * (x,y) = (ax-by, bx+ay)

    According to this definition, (0,1)*(0,1) = (-1,0) and is then denoted i^2 by construction. Rewriting (a,b) as a+bi and calling the plane C rather than R^2, the operations hold:

    (a+bi) + (x+yi) = (a+x) + (b+y)i
    (a+bi) * (x+yi) = (ax-by) + (ay+bx)i

    And if b=0 in a+bi then a+0i = a which is the real part of the complex number and is a real number, also known as (a,0) in C.
     
    Last edited: Sep 22, 2009
  4. Sep 22, 2009 #3

    tiny-tim

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    Hi I_am_no1! :smile:

    (have a square-root: √ :wink:)
    Not really …

    a complex number can be written in standard form as a + ib, or in polar form as re, and they correspond to cartesian and polar coordinates on an argand diagram.
    Yes, the x axis is all the real numbers, and the y axis is all the imaginary numbers …

    for that reason, they're also called the real axis and the imaginary axis. :smile:
     
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