Answer:
[tex]\sqrt{-3}= i\sqrt{3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{-3[/tex]
Required
Express as imaginary unit
[tex]\sqrt{-3[/tex]
Express 3 as 3 * -1
[tex]\sqrt{3 * -1[/tex]
Split the radical to 2
[tex]\sqrt{3} * \sqrt{-1[/tex]
In complex numbers:
[tex]\sqrt{-1} = i[/tex]
So, the expression:
[tex]\sqrt{3} * \sqrt{-1}[/tex]
becomes
[tex]\sqrt{3} * i[/tex]
[tex]i\sqrt{3}[/tex]
Hence:
[tex]\sqrt{-3}= i\sqrt{3}[/tex]
