Question

How to solve this problem

Answer 1

Solving the radical
`\pm√(-81)` we get
`\mathbf{\pm9 \ i}`

Explanation:

We need to express the radical
`\pm√(-81)` using the imaginary unit i

Prime factors of 81 are: 3x3x3x3

and
`√(-1)=i`

Solving:

`\pm√(-81)\\=\pm√(81)√(-1)\\=\pm√(3*3*3*3)i\\ =\pm√(3^2*3^2)i\\=\pm3*3\ i\\=\pm9 \ i`

So, Solving the radical
`\pm√(-81)` we get
`\mathbf{\pm9 \ i}`