# [SOLVED] limits Q help needed.

• May 29th 2009, 02:35 PM
i_zz_y_ill
[SOLVED] limits Q help needed.
Hia , does anyone know how my answer book got this answer for what is $\displaystyle Im(\frac{z}{\overline{z}})=\frac{2xy}{x^2+y^2}$ 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!
• May 29th 2009, 02:41 PM
TheEmptySet
Quote:

Originally Posted by i_zz_y_ill
Hia , does anyone know how my answer book got this answer for what is $\displaystyle Im(\frac{z}{\overline{z}})=\frac{2xy}{x^2+y^2}$ 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!

$\displaystyle \frac{z}{\bar z}=\frac{z\cdot z}{\bar z z}=\frac{z^2}{z\bar z}$

Now if $\displaystyle z=x+iy$

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

Now if we take the immaginary part we get you get what you want (Wink)