Answer:
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate of the denominator to eliminate the square root from the denominator. The conjugate of 3 + √(6i) is 3 - √(6i).
(2 - √(2i))/(3 + √(6i)) * (3 - √(6i))/(3 - √(6i))
2. Simplify the expression by applying the FOIL method (First, Outer, Inner, Last) to the numerator and denominator.
Numerator: 2 * 3 - 2 * √(6i) - √(2i) * 3 + √(2i) * √(6i)
= 6 - 2√(6i) - 3√(2i) + √(12i^2)
= 6 - 2√(6i) - 3√(2i) + √(12 * -1) (since i^2 = -1)
= 6 - 2√(6i) - 3√(2i) + √(-12)
= 6 - 2√(6i) - 3√(2i) + √(-1)√(12)
= 6 - 2√(6i) - 3√(2i) + i√(12)
Denominator: (3)^2 - (√(6i))^2
= 9 - 6i
3. Simplify the expression further by combining like terms.
= (6 - 2√(6i) - 3√(2i) + i√(12))/(9 - 6i)
Now, the expression (2 - √(2i))/(3 + √(6i)) is simplified as (6 - 2√(6i) - 3√(2i) + i√(12))/(9 - 6i).