Explanation
We need to find simplest form of $$\dfrac{10-\sqrt{-12}}{1-\sqrt{-27}}$$
$$=\dfrac{10-2i\sqrt{3}}{1-3i\sqrt{3}}$$
Taking conjugate, we get
$$=$$ $$\dfrac{10-2\sqrt{-3}}{1-3\sqrt{-3}}\times \dfrac{1+3i\sqrt{3}}{1+3i\sqrt{3}}$$
$$=$$ $$\dfrac{\frac{10-2\sqrt{-3}}{1-3\sqrt{-3}}}{1^2-(3i\sqrt{3})^2}$$
$$=$$ $$\dfrac{10+30i\sqrt{3}-2i\sqrt{3}-18i^2}{28}$$
$$=$$ $$\dfrac{10+28i\sqrt{3}+18}{28}$$
$$=$$ $$\dfrac{28(1+i\sqrt{3})}{28}$$
$$=$$ $$1+i\sqrt{3}$$
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