The real part of the impedance at the stub location must match the transmission line characteristic impedance

The imaginary part of the impedance at the stub location must equal 0

$$\begin{gathered} \mathrm{restart}\: \\ \mathrm{assume}\left(\mathrm{d}\,\mathrm{real}\,\mathrm{l}\,\mathrm{real}\right) \end{gathered}$$

$\mathrm{Z\_\_0}≔50 ⟦\mathrm{ohms}⟧\:$

$\mathrm{Z\_\_L}≔\left(35- 47.5 \mathrm{I}\right)⟦\mathrm{ohms}⟧\:$

$\mathrm{\λ}≔1⟦\mathrm{m}⟧\:$

$\mathrm{\β}≔2\cdot \mathrm{\π}\/\mathrm{\λ}\:$

$\mathrm{circuit}≔\frac{\mathrm{Z\_\_0}\cdot \cos \left(\mathrm{\β}\cdot \mathrm{d}\right)\+\mathrm{I}\cdot \mathrm{Z\_\_L}\cdot \sin \left(\mathrm{\β}\cdot \mathrm{d}\right)}{\mathrm{Z\_\_L}\cdot \cos \left(\mathrm{\β}\cdot \mathrm{d}\right)\+\mathrm{I}\cdot \mathrm{Z\_\_0}\cdot \sin \left(\mathrm{\β}\cdot \mathrm{d}\right)}-\mathrm{I}\cdot \cot \left(\mathrm{\β}\cdot \mathrm{l}\right)\:$

$\mathrm{fsolve}\left(\left\{\mathrm{Re}\left(\mathrm{circuit}\right)\=1\, \mathrm{Im}\left(\mathrm{circuit}\right)\=0\right\}\,\left\{\mathrm{l}\=0.1 ⟦\mathrm{m}⟧\,\mathrm{d}\=0.1 ⟦\mathrm{m}⟧\right\}\right)$

$\left\{\mathrm{d~}=58.94\times {10}^{-3}⟦m⟧\,\mathrm{l~}=111.18\times {10}^{-3}⟦m⟧\right\}$