Let \( [x;y]\in\mathbb{R}\times\mathbb{R} \), \( z_1 = 5 + xy\,\mathrm{i} \) and \( z_2 = x + y - 4\,\mathrm{i} \). Find all \( [x;y] \) such that \( z_1 \) and \( z_2 \) are the complex conjugates.
Given the complex numbers \( a=\sqrt2\left(\cos160^{\circ}+\mathrm{i}\cdot\sin160^{\circ}\right) \), \( b=3\sqrt2\left(\cos150^{\circ}+\mathrm{i}\cdot\sin150^{\circ}\right) \) and \( c=2\left(\cos240^{\circ}+\mathrm{i}\cdot\sin240^{\circ}\right) \), evaluate \( a\cdot b\cdot c \).