1. Not finding help here? Sign up for a free 30min 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!

Complex Solutions

  1. Mar 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Find all complex solutions to [itex]\bar{z}[/itex] = z


    2. Relevant equations

    z = x + iy and [itex]\bar{z}[/itex] = x - iy

    3. The attempt at a solution
    What does it mean by find all complex solutions?

    [itex]\bar{z}[/itex] = z
    0 = x + iy - x + iy
    0 = 2iy
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 12, 2012 #2
    Two complex numbers are only equal if their real parts are equal and their imaginary parts are equal so you may have to equate real and imaginary parts to find the values of x and y.
     
  4. Mar 12, 2012 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    If 0 = 2iy, then ...
    1. What must x be for this to be true?

    2. What must y be for this to be true?​
     
  5. Mar 13, 2012 #4
    2y = 0 and x=0
     
  6. Mar 13, 2012 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    How do you arrive at "x= 0" from an equation that does not have an "x" in it??
     
  7. Mar 13, 2012 #6
    Well the basic form is x + iy, so we know the x part of the complex number must be equal to zero if it's not there.
     
  8. Mar 13, 2012 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Look at the equation (from post #1):
    0 = x + iy - x + iy​
    Is there any x that will not satisfy this, if y=0 ? If there is such an x, what is it ?
     
  9. Mar 14, 2012 #8
    Yes when I say x=0 it means that the 'real part' of the solution is 0
     
  10. Mar 14, 2012 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, and as you have been told repeatedly, that is wrong. The equation 2iy= 0 does NOT say "x= 0 because x isn't there". The fact that x is not in that equation means that the equation does not tell you anything about x. Suppose z= 4+ 0i. What is [itex]\overline{z}[/itex]?
     
  11. Mar 14, 2012 #10

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Good point. I really hadn't thought of that!:redface: Okay, how about a simple sequence of real numbers?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex Solutions
  1. Complex Solutions (Replies: 1)

  2. Complex Solutions (Replies: 7)

Loading...