1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why the point of x + iy would be (x, y) ?
  1. Is x^iy possible? (Replies: 3)

Loading...