Find the product and enter the real and imaginary parts below. Note that you do not need to type in the since it is already given to you. Simplify your square roots as much as possible.
sqrt-27((sqrt-5)-(sqrt-11))
To find the product of sqrt(-27)((sqrt(-5)) - (sqrt(-11))), we can simplify the square roots first.
Let's consider the first square root, sqrt(-27).
The square root of a negative number is not a real number, so we need to express it using the imaginary unit, 'i'.
We can rewrite sqrt(-27) as sqrt(27*(-1)).
Next, let's simplify the square root of 27.
The square root of 27 can be expressed as sqrt(9 * 3).
Taking the square root of 9, we get 3.
So, sqrt(27) = sqrt(9 * 3) = sqrt(9) * sqrt(3) = 3 * sqrt(3).
Now, let's go back to sqrt(-27) = sqrt(27*(-1)).
We can substitute sqrt(27) with 3 * sqrt(3) and rewrite it as 3 * sqrt(3) * sqrt(-1).
Moving on to the second square root, sqrt(-5), we can use the same approach.
Rewrite sqrt(-5) as sqrt(5*(-1)).
Then, simplify sqrt(5) as much as possible.
Now, let's consider the third square root, sqrt(-11).
Rewrite sqrt(-11) as sqrt(11*(-1)).
Simplify sqrt(11) as much as possible.
So, the expression now becomes:
(3 * sqrt(3) * sqrt(-1)) - (sqrt(5) * sqrt(-1)) * sqrt(11*(-1)).
We can now distribute the sqrt(-1) to simplify further:
(3 * sqrt(3) * i) - (sqrt(5) * i) * sqrt(11) * i.
Next, multiply the terms:
3 * sqrt(3) * i - sqrt(5) * i * sqrt(11) * i.
To simplify further, remember that i * i = -1, so we can rewrite i * i as -1.
Finally, the expression becomes:
3 * sqrt(3) * i - sqrt(5) * i * sqrt(11) * i = 3 * sqrt(3) * i + sqrt(5) * sqrt(11) * (-1).
Therefore, the product of sqrt(-27)((sqrt(-5)) - (sqrt(-11))) is 3 * sqrt(3) * i - sqrt(5) * sqrt(11).