Which of the following re-expresses the negative square root -6√-20 as a complex number in the standard form a + bi?
-12i√5
-12√5
2i√5
-12√5i
To re-express the negative square root -6√-20 as a complex number in the standard form a + bi, we need to simplify it using the properties of imaginary numbers.
First, let's simplify the square root:
-6√-20 = -6√(-1 * 4 * 5)
We can break down the square root into two parts:
-6 * √-1 * √4 * √5
The square root of -1 is denoted as "i", and the square root of 4 is 2. Therefore, we have:
-6 * i * 2 * √5
Simplifying further:
-12i√5
So, the re-expression of -6√-20 in the standard form a + bi is -12i√5.
Therefore, the correct option is: -12i√5.
The square root of -20 is equal to the square root of -1 times the square root of 20. We know that the square root of -1 is equal to the imaginary unit i. Therefore, the square root of -20 can be written as i times the square root of 20.
So, -6√-20 can be written as -6i√20.
Simplifying further, we have -6i times the square root of 4 times the square root of 5. Since the square root of 4 is equal to 2, we can rewrite the expression as -12i times the square root of 5.
Finally, in the standard form a + bi, where a and b are real numbers, the real part is -12 times the square root of 5 and the imaginary part is 0. So, the re-expression of -6√-20 as a complex number in standard form is -12√5 + 0i.
To re-express the negative square root -6√-20 as a complex number in standard form, we need to simplify it.
First, let's simplify the expression inside the square root:
√(-20) = √(-1 * 20) = √(-1) * √(20) = i * √20 = i√20.
Next, let's combine the simplified square root with the coefficient:
-6√(-20) = -6i√20.
Therefore, the correct re-expression of -6√(-20) as a complex number in standard form is -6i√20.
None of the given options -12i√5, -12√5, 2i√5, -12√5i represent the correct re-expression.