Which of the following re-expresses the negative square root sqrt(- 40) as a complex number in the standard form a + b * i' (1 point)

2sqrt(10)

2isqrt(10)

2sqrt(10i)

4isqrt(10)

1 answer

To express \(\sqrt{-40}\) in the standard form \(a + bi\), we start by rewriting it as:

\[ \sqrt{-40} = \sqrt{-1 \cdot 40} = \sqrt{-1} \cdot \sqrt{40} = i \cdot \sqrt{40} \]

Next, we can simplify \(\sqrt{40}\):

\[ \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10} \]

Thus, we have:

\[ \sqrt{-40} = i \cdot 2\sqrt{10} = 2\sqrt{10} i \]

This can be rewritten in the standard form:

\[ 0 + 2\sqrt{10} i \]

Therefore, the complex number in standard form is \(0 + 2\sqrt{10} i\), which corresponds to the answer:

\[ \boxed{2i\sqrt{10}} \]