How to Simplify Backward Impedance Matching Equations?

[inter060708]

Homework Statement

https://scontent-lax3-1.xx.fbcdn.net/v/t34.0-12/14804959_10155526179417281_80533891_n.png?oh=649ee14155ac558b21c6553f003e418b&oe=5809EAA0

Homework Equations

The Attempt at a Solution

1) I determined the input impedance of the first transmission line (Zin1).
2) I calculated the equivalent impedance (Zeq) of 50 Ohms and Zin1
3) Found corresponding impedance of Gamma_s (Zs)
4) I switched the position of Zs with Zeq
5) Replaced Zs with its complex conjugate (Zs*)
6) Found input impedance of Zeq at length -l2
7) Set it equal to Zs*, solve for real and imaginary coefficients to get l1 and l2

The equation turns out to be very complicated and I am sure there is easier way, please help. Thank you
https://scontent-lax3-1.xx.fbcdn.net/v/t35.0-12/14647238_10155526274642281_613988889_o.jpg?oh=461d284cb7c90bcccfc46c1e3d960cb8&oe=5808D15D

 

[berkeman]

Homework Statement

https://scontent-lax3-1.xx.fbcdn.net/v/t34.0-12/14804959_10155526179417281_80533891_n.png?oh=649ee14155ac558b21c6553f003e418b&oe=5809EAA0

Homework Equations

The Attempt at a Solution

1) I determined the input impedance of the first transmission line (Zin1).
2) I calculated the equivalent impedance (Zeq) of 50 Ohms and Zin1
3) Found corresponding impedance of Gamma_s (Zs)
4) I switched the position of Zs with Zeq
5) Replaced Zs with its complex conjugate (Zs*)
6) Found input impedance of Zeq at length -l2
7) Set it equal to Zs*, solve for real and imaginary coefficients to get l1 and l2

The equation turns out to be very complicated and I am sure there is easier way, please help. Thank you
https://scontent-lax3-1.xx.fbcdn.net/v/t35.0-12/14647238_10155526274642281_613988889_o.jpg?oh=461d284cb7c90bcccfc46c1e3d960cb8&oe=5808D15D

Your picture is basically unreadable. Could you type your work into the forum instead? There is a LaTeX primer in the Help/How To section of the forum -- click on INFO at the top of the page.