Question

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)

2i * sqrt(10)

2sqrt(10i)

4i * sqrt(10)

Answer 1

To express \(\sqrt{-40}\) as a complex number in the standard form \(a + bi\), we can follow these steps:

1. Recognize that \(\sqrt{-40}\) can be rewritten using the property of square roots:
\[
\sqrt{-40} = \sqrt{40} \cdot \sqrt{-1} = \sqrt{40} \cdot i
\]

2. Now, calculate \(\sqrt{40}\):
\[
\sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10}
\]

3. Therefore, we can express \(\sqrt{-40}\) as:
\[
\sqrt{-40} = 2\sqrt{10} \cdot i = 0 + 2\sqrt{10}i
\]

This matches the form \(a + bi\) with \(a = 0\) and \(b = 2\sqrt{10}\).

Thus, the re-expressed form of \(\sqrt{-40}\) is:
\[
\boxed{2i \sqrt{10}}
\]

This corresponds to the option **2i * sqrt(10)**.