Answer :

[tex]2 - \sqrt{-4} - 3 + \sqrt{-16} [/tex]
[tex]= 2 - i\sqrt{4} - 3 + i\sqrt{16} [/tex]
[tex]= 2 - 2i - 3 + 4i [/tex]
[tex]= -1 + 2i [/tex]
AL2006
The square root of (-4) = square root of  (-1) x (4) = 2i

The square root of (-16) = square root of (-1) x (16) = 4i

So now you have the sum of  (2 - 2i) and (-3 + 4i).

The real part of the sum is (2 - 3) = -1

The imaginary part of the sum is ( -2i + 4i ) = +2i

The whole sum is    -1 + 2i .