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Homework Help: Find the real and imaginary parts of (1-z)/(i+z)

  1. Oct 8, 2016 #1
    Member advised that the homework template is required.
    Hey there! Need help figuring this out:
    Find the real and imaginary parts of [tex]\frac{1-z}{i+z}[/tex]

    What I've tried was to notice that [tex]z\bar{z}=|z|^2[/tex], thence [tex]\frac{1-z}{i+z}=\frac{(1-z)}{(i+z)}\frac{(\overline{i+z})}{(\overline{i+z})}=\frac{(1-z)(i+\overline{z})}{|i+z|^2}=\frac{\overline{z}+i(z-1)-|z|^2}{|i+z|^2}[/tex]

    But now I'm stuck. Any help is appreciated. Thanks in advance.
    Last edited by a moderator: Oct 8, 2016
  2. jcsd
  3. Oct 8, 2016 #2


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    Science Advisor
    Homework Helper
    Gold Member

    What sort of answer are you looking for? Usually you would have ##z = x + iy## and would express the real and imaginary parts of the expression in terms of ##x## and ##y##.
  4. Oct 8, 2016 #3


    Staff: Mentor

    Let z = x + iy, and write the above as ##\frac{1 - x - iy}{i + x + iy} = \frac{1 - x - iy}{x + i(y + 1)}##, and then multiply by 1 in the form of the conjugate over itself.

    Also, in future posts, please don't delete the homework template - it's not optional.
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