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Equation of a Line

  1. Jul 2, 2007 #1
    Just want a check of this please:

    We have a complex equation of the form az+bz*+c=0
    where a, b and z are complex #s, c is real...
    If you take the real and imaginary parts of such an equation you obtain two linear equations in x and y, whose solutions of each gives rise to a line (L_1 and L_2 respectively)....
    The set then, of solutions, is L_1 unison L_2

    Now, the set of solutions of the complex equation is either empty, a point, or a line....................the book gives these 3 examples as each case:
    z + z* = i

    z+2z* = 0

    z+z* = 0


    I don't understand how z+z*=0 is a line... for we in fact have
    RE(Z+Z*)=2x=0
    IM(Z+Z*)= 0y = 0
    which then gives rise to a point solution does it not??

    if it was z+z* = c say, then i could see that having a line of solutions but as it is, i reckon the book has made an error..... is this the case???

    (perhaps i have confused the issue and if that is the case maybe then you coudl point out how my thinking is wrong)

    THANKYOU :)
     
  2. jcsd
  3. Jul 2, 2007 #2
    x=0 and y=0 refer not to points but to the y- and x- axis respectively, which you can see are lines, it's like saying for every value of y, x=0 or any constant so it's not a point but infact a line. I hope this explanation was coherent.
     
  4. Jul 2, 2007 #3

    uart

    User Avatar
    Science Advisor

    It does not.

    Yes 2x = 0 only has the solution that x=0. However 0y = 0 does not just have the solution that y=0, rather it has the solution y=anything. This makes the solutuion the entire imaginary axis (x=0), does that make sense.
     
  5. Jul 2, 2007 #4
    Yeah it makes sense, thanks a lot the both of you...
    Physicsforums again proves a real gem..
     
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