Show me the steps to solve:

$1)$ A load has impedance Z$\_$L $=$ Z$\_0+$ j c$*$Z$\_0,$ where Z$\_0$ is the characteristic impedance of the transmission line to which it is connected, and $"$c$"$ is a real constant.

$($a$)$ Determine the values $$of c such that the magnitude of the reflection coefficient at the load is equal to $0\mathrm{.}5.$

$($b$)$ For each solution found, calculate the phase of the reflection coefficient at the corresponding load $($in degrees$).$

Note $1$: Question corresponding to the subjects of "Microwave Engineering" and "High Frequency Electronic Circuits" or "Electromagnetism".

Note $2$: Z$\_0($characteristic impedance$)$ would be $"$Z with subscript zero"

Note $3$: Z$\_$L $($load impedance$)$ would be $"$Z with subscript L$"$

Note $4$: $"*"$ would be the multiplication$/$product symbol between the terms