Question

Simplify: - ( root of -7/4) -( root of -1/7)Ans given: [ -9( root of 7 ) i ]/14

Answer 1

$$\begin{gathered} -\sqrt{-\frac{7}{4}}-\sqrt{-\frac{1}{7}} \\ =-\sqrt{\frac{7}{4}{\mathrm{i}}^2}-\sqrt{\frac{{\mathrm{i}}^2}{7}}\left[\mathrm{as},{\mathrm{i}}^2=-1\right] \\ =-\frac{\sqrt{7}}{2}\mathrm{i}-\frac{\mathrm{i}}{\sqrt{7}} \\ =\frac{-7\mathrm{i}-2\mathrm{i}}{2\sqrt{7}} \\ =-\frac{9\mathrm{i}}{2\sqrt{7}} \\ =-\frac{9\mathrm{i}}{2\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}} \\ =-\frac{9\sqrt{7}\mathrm{i}}{14} \end{gathered}$$