Verified answer

2 + (√-4) - 2(√-3) - (√-3)(√-4)

(2 + (√-3)(√-4)) + ( 2 -2√3)(i) (this is where u went wrong)

instead of subtracting ( - (√-3)(√-4)) you added it

[ 1 - √ ( 3 i ² ) ] [ 2 + √ ( 4 i ² ) ]

[ 1 - i √3 ] [ 2 + 2 i ]

2 + ( 2 - 2√3 i ) + 2 √3

( 2 + 2 √3 ) + ( 2 - 2√3 i )

You changed a minus to a plus from the second line to the third line.

Look at the sign for the (√-3)(√-4) term.

look at your third line. dont try do to much in one step

2 + sqrt -4 - 2 sqrt -3 - sqrt -3 sqrt -4

2 + 2 (sqrt -1) -2 (sqrt 3)(sqrt -1) - 2 (sqrt 3) (sqrt -1) (sqrt -1)

2 + 2i -2(sqrt 3)i + 2 (sqrt 3) as i^2 is -1

which is your answer, you just messed up a sign in your rearanging in line three

queston is (1-root3i)(2+2i) = 2- 2root3 i + 2i - 2 root 3 ixi = i(2- 2root3) + 2 + 2 root 3 ( since ix i = -1)

which is d ans,,,,,,,, sorry dude cud nt find the sign of square root bt u will under stand

when you commuted on the second and third lines

- (sqrt(-3))(sqrt(-4))

became

+(sqrt(-3))(sqrt(-4))

that is why the sign mistake in your answer