Simplify (Real Numbers) (2 + sqrt(-3)/2))(2 - sqrt(-3)/2))

Question

These are the answer choices

 

1/4

7/4

13/4

Answer 1

 Hi Gabby,

Multiplying this out using the FOIL technique you should multiply 2x2 then the outer and inner terms sum to 0 and that leaves only the last terms which are +-√-3/2 with the 2 outside of the square root sign (Thanks Dave) giving 13/4

Answer 2

I concur.  This is like (a + b)(a - b) = a² - b²

 

We get 2² - (√(-3)/2)² = 4 - (-3/4) = 4 + 3/4 = 19/4

 

 

√-3 x √-3 = -3. The normal rules of a negative times a negative being positive do not apply, because √-3 is not itself a negative.

Answer 3

(2+[√-3]/2)(2-[√-3]/2)

4-[√-3][√-3]/(2)(2)

4-(-3)/4

4+(3/4)

19/4 should be the answer if it's √(-3)/2

I think maybe somebody made a mistake thinking √-3*√-3=3, then you would incorrectly get 4-3/4=3 1/4=13/4