Answer:
[tex]\frac{-5-\sqrt{-48}}{40}[/tex] in terms of i is: [tex]\frac{-1}{8}-\frac{i\,\sqrt{3}}{10}[/tex]
Step-by-step explanation:
[tex]\frac{-5-\sqrt{-48}}{40}[/tex]
We know that [tex]\sqrt{-1} = i[/tex]
so,
[tex]\frac{-5-\sqrt{48}i}{40}[/tex]
Now solving:
[tex]=\frac{-5}{40}-\frac{i\,\sqrt{48}}{40}\\=\frac{-1}{8}-\frac{i\,\sqrt{2*2*2*2*3}}{40}\\=\frac{-1}{8}-\frac{i\,\sqrt{2^2*2^2*3}}{40}\\=\frac{-1}{8}-\frac{2*2\,i\,\sqrt{3}}{40}\\=\frac{-1}{8}-\frac{4\,i\,\sqrt{3}}{40}\\=\frac{-1}{8}-\frac{i\,\sqrt{3}}{10}[/tex]
So, [tex]\frac{-5-\sqrt{-48}}{40}[/tex] in terms of i is: [tex]\frac{-1}{8}-\frac{i\,\sqrt{3}}{10}[/tex]
