$$ \begin{equation} \begin{split} \left(-\frac{1}{3} \cdot \sqrt{6} \cdot i \right) ^ 2& = \frac{-1^2}{3^2} \cdot 6 \cdot i^2\\ & = \frac{1}{9} \cdot \frac{6}{1} \cdot -1\\ & = \frac{6}{9} \cdot -1\\ & = \frac{2}{3} \cdot -1\\ & = -\frac{2}{3} \end{split} \end{equation} $$ ====== 1.2c ====== $$ \begin{equation} \begin{split} \left( \frac{1}{2} \cdot \sqrt{4} \cdot i \right) ^ 2 & = \frac{1^2}{2^2} \cdot 4 \cdot i^2\\ & = \frac{1}{4} \cdot 4 \cdot i^2\\ & = \frac{1}{4} \cdot \frac{4}{1} \cdot -1\\ & = 1 \cdot -1\\ & = -1\\ \end{split} \end{equation} $$