Simplify the follwing... (2+√-12)(6-√5)?

Question

please explain how it's done? Thank you it would mean a lot

(2+√-12)(6-√5)?

3/ 4-√-6

Answer 1

(1).

The expression is (2 + √-12)(6 - √5)

Rewrite √-12 = √(i²*4*3)          [ Since i² = -1]

                     = 2i√3

(2 + √-12)(6 - √5) = (2 + 2i√3)(6 - √5)

                             = 12 - 2√5 + 12i√3 - 2i√15

                             = (12 - 2√5) + i(12√3 - 2√15)

(2).

The expression is 3/(4 - √-6).

Rewrite √-6 = √(i²*6)          [ Since i² = -1]

                     = i√6.

3/(4 - √-6) = 3/(4 - i√6)

Divide the numerator and denominator by (4 + i√6).

                 = 3(4 + i√6) /(4 - i√6)(4 + i√6)

Apply Sum and Difference of Same Terms : (u + v)(u - v) = u² - v².

                 = (12 + 3i√6) /[4² - (i√6)²]

                 = (12 + 3i√6) /(16 - i²6)

                 = (12 + 3i√6) /20          [ Since i² = -1]

                 = 3/5 + i(3√6/20).