Question

(-3+2iroot48)(-5-4iroot12)
HELP PLEASE

Answer 1

-16 i sqrt(3) + 207

Explanation:

Simplify the following:

(2 i sqrt(48) - 3) (-4 i sqrt(12) - 5)

sqrt(12) = sqrt(2^2×3) = 2 sqrt(3):

(2 i sqrt(48) - 3) (-4 i×2 sqrt(3) - 5)

-4×2 = -8:

(2 i sqrt(48) - 3) (-8 i sqrt(3) - 5)

Factor -1 from -8 i sqrt(3) - 5:

(2 i sqrt(48) - 3)×-(8 i sqrt(3) + 5)

sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):

-(2 i×2^2 sqrt(3) - 3) (8 i sqrt(3) + 5)

2^2 = 4:

-(2 i×4 sqrt(3) - 3) (8 i sqrt(3) + 5)

2×4 = 8:

-(8 i sqrt(3) - 3) (8 i sqrt(3) + 5)

-(8 i sqrt(3) - 3) = -8 i sqrt(3) + 3:

-8 i sqrt(3) + 3 (8 i sqrt(3) + 5)

(-8 i sqrt(3) + 3) (8 i sqrt(3) + 5) = 3×5 + 3×8 i sqrt(3) + -8 i sqrt(3)×5 + -8 i sqrt(3)×8 i sqrt(3) = 15 + 24 i sqrt(3) - 40 i sqrt(3) + 192 = -16 i sqrt(3) + 207:

Answer: -16 i sqrt(3) + 207

Answer 2

For this case we must simplify the following expression:

`(-3 + 2i \sqrt {48}) (- 5-4i \sqrt {12})`

Rewriting:

`(-3 + 2i \sqrt {4 ^ 2 * 3}) (- 5-4i \sqrt {2 ^ 2 * 3}) =\\(-3 + 2 * 4i \sqrt {3}) (- 5-4 * 2i \sqrt {3}) =\\(-3 + 8i \sqrt {3}) (- 5-8i \sqrt {3}) =`

We apply distributive property:

`- * - = +\\- * + = -\\15 + 24i \sqrt {3} -40i \sqrt {3} - (8i \sqrt {3}) ^ 2 =\\15 + 24i \sqrt {3} -40i sqrt {3} -64i ^ 2 * 3 =`

We have to
`i ^ 2 = -1:`

`15 + 24i \sqrt {3} -40i \sqrt {3} + 192 =`

Adding similar terms:

`207-16i \sqrt {3}`

answer:

`207-16i \sqrt {3}`