Question

Perform the indicated operations. Do the root of -48 in terms of i please

Answer 1

`(-5-√(-48))/(40)` in terms of i is:
`(-1)/(8)-(i\,√(3))/(10)`

Explanation:

`(-5-√(-48))/(40)`

We know that
`√(-1) = i`

so,

`(-5-√(48)i)/(40)`

Now solving:

`=(-5)/(40)-(i\,√(48))/(40)\\=(-1)/(8)-(i\,√(2*2*2*2*3))/(40)\\=(-1)/(8)-(i\,√(2^2*2^2*3))/(40)\\=(-1)/(8)-(2*2\,i\,√(3))/(40)\\=(-1)/(8)-(4\,i\,√(3))/(40)\\=(-1)/(8)-(i\,√(3))/(10)`

So,
`(-5-√(-48))/(40)` in terms of i is:
`(-1)/(8)-(i\,√(3))/(10)`