\(\displaystyle{i}\frac{\sqrt{{6}}}{{{i}\sqrt{{3}}\cdot{i}\sqrt{{4}}}}=-{i}\frac{\sqrt{{6}}}{{2}}\sqrt{{3}}=-{i}\frac{\sqrt{{\frac{{6}}{{3}}}}}{{2}}=-{i}\frac{\sqrt{{2}}}{{2}}\). So \(\displaystyle{a}={0}{\quad\text{and}\quad}{b}=-\frac{\sqrt{{2}}}{{2}}\) for a+ib.

Therefore \(\displaystyle{a}={0}{\quad\text{and}\quad}{b}=-√\frac{{2}}{{2}}{\quad\text{or}\quad}-\frac{{1}}{

Therefore \(\displaystyle{a}={0}{\quad\text{and}\quad}{b}=-√\frac{{2}}{{2}}{\quad\text{or}\quad}-\frac{{1}}{