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

1 answer

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.