Verified answer

2(√(1 +√-3)(1 - √-3))

= 2√(1 - (-3))

= 2*2

= 4

2 * ( √(1 +√-3) * (1 - √-3) )

= 2 * ( √(1 +√-3) * √(1 - √-3) * √(1 - √-3) )

= 2 * √( (1 +√-3) * (1 - √-3) * (1 - √-3) )

= 2 * √( (1 + 3) * (1 - √-3) )

= 2 * √( 4 * (1 - √-3) )

= 4 * √(1 - √-3)

If you meant...

2 * √( (1 +√-3) * (1 - √-3) )

=2*√(1--3)

=2 * ±2

=±4, though we should be able to take +4 as the result, given no indication that the negative is needed, i.e. the question wasn't written 2 * -√( (1 +√-3) * (1 - √-3) )

2(√(1 +√-3)(1 - √-3)) < ------------------- Multiply

= 2(1 - -3) <------- a difference of two sqiuares

= 2(4) <--------------Subtracting a negative

= 8

inside or a square root cannot be negative