[填空题]
Consider the complex numbershy x8p xw tv:2;g1 pfpwbh.25bln8tk8n7tqy3tahqu 1y:6gk1d d n2o8 $u=1+2 \mathrm{i} and v=2+\mathrm{i}$ .
1. Given that $\frac{1}{u}+\frac{1}{v}=\frac{6 \sqrt{2}}{w}$ , express w in the form $a+b \mathrm{i}$ where $a, b \in \mathbb{R}$ .$a \sqrt{b}+c \sqrt{d} \mathrm{i}$ a = b = c = d =
2. Find $w^{*}$ and express it in the form r $e^{\mathrm{i} \theta}$ .$a e^{-i \frac{\pi}{b}}$ a = b =
