Question

How do you evaluate `7\sqrt { - 63} - 5\sqrt { - 28}` using imaginary numbers?

Answer 1

`sqrt(-63) = sqrt((9)(7)(-1)) = 3sqrt7i`

`sqrt(-28) = sqrt((4)(7)(-1)) = 2sqrt7i`

So,

`7sqrt(-63) - 3sqrt(-28) = 7(3sqrt7i)-5(2sqrt7i)`

`= 21sqrt7i-10sqrt7i`

`= 11sqrt7i`