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!

Homework Help: Algebra in the complex plane

  1. Jan 12, 2017 #1
    1. The problem statement, all variables and given/known data
    Solve each equation for z=a+ib
    [itex] z^{*2}=4z [/itex]
    where z* is the complex conjugate

    3. The attempt at a solution
    I wrote z and z* in terms of x and iy , and tried solving for x and y, but I get quartic terms for y, it doesnt look like it will boil down, It was like over 2 pages of algera, I dont think that is how it is supposed to be done, I tired some alternative forms of the modulus and it didnt go anywhere, Are my approaches the right way, or do I need some clever substitution, or can it be solved with Eulers formula ?
  2. jcsd
  3. Jan 12, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Show us the equations in x and y that you actually get. What you are claiming sounds wrong to me.
  4. Jan 12, 2017 #3


    Staff: Mentor

    If z = a + bi, then ##\bar{z} = a - bi##
    If I substitute these into the given equation, I don't get a quartic, but I do get a solution fairly quickly. Please show what you did.
  5. Jan 12, 2017 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I would automatically use the polar form here.
  6. Jan 12, 2017 #5


    Staff: Mentor

    That's a possibility, but it isn't necessary here.
  7. Jan 12, 2017 #6
    oh ok I think I got it
    sub in x+iy and x-iy
    then equate real and imaginary
    Real = [itex] x^2+y^2=4x [/itex]
    Im = [itex] -2xy=4y [/itex]
    I solved for x then put it in the other equation, then I solved for y,
    and I got the answer in the back of the book, thanks for your posts
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted