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