Smith chart tutorial question
For the real component of Γ, Zl = 50Ω (1+(-0.3)) / (1-(-0.3)) = 26.9Ω
  
  For the imaginary component: Zl = 50Ω (1+i0.4) / (1-i0.4) = 116.67 Ω


You can't split up the real and imaginary components like this. Your equation needs to be

\$Z_l=50 \frac{1 + (-0.3+0.4j)}{1-(-0.3+0.4j)}\$

If you then simplify this you get to the answer they provided.

One of the nice things about a Smith chart is that you can easily convert between reflection and impedance. If you had a smith chart with a grid on it, you could plot this reflection and directly read off the answer without needing to do any math.