A $50$ lossless line is driven by a source with $v_g(t)=10cos(8{10}^{7}t+30)V$ and $Z_g=50.$ If the line is $0\mathrm{.}75$ long and terminated in a load $Z_L=(50-j25),$ answer the following questions.

$($a$)$ What is the reflection coefficient at the load? Your answer must be in polar form.

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$($b$)$ What is the input impedance? Your answer must be in both polar and Cartesian forms.

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$($c$)$ What is the input voltage? Your answer must be in polar form.

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$($d$)$ What is the time domain input voltage $v_i(t)?$

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