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Math Help - [SOLVED] limits Q help needed.

  1. #1
    Member i_zz_y_ill's Avatar
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    [SOLVED] limits Q help needed.

    Hia , does anyone know how my answer book got this answer for what is Im(\frac{z}{\overline{z}})=\frac{2xy}{x^2+y^2} really confused? I actually think ill be posting quite a few posts in the next few days i hope i dont get too anooying thanks for your help!
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  2. #2
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    Quote Originally Posted by i_zz_y_ill View Post
    Hia , does anyone know how my answer book got this answer for what is Im(\frac{z}{\overline{z}})=\frac{2xy}{x^2+y^2} really confused? I actually think ill be posting quite a few posts in the next few days i hope i dont get too anooying thanks for your help!
    \frac{z}{\bar z}=\frac{z\cdot z}{\bar z z}=\frac{z^2}{z\bar z}

    Now if z=x+iy

    \frac{(x+iy)^2}{(x+iy)(x-iy)}=\frac{x^2-y^2+i(2xy)}{x^2+y^2}=\frac{x^2-y^2}{x^2+y^2}+i\frac{2xy}{x^2+y^2}

    Now if we take the immaginary part we get you get what you want
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