To re-express \(-\sqrt{-20}\) as a complex number in standard form \(a + bi\), we first recognize that \(-20\) can be expressed as \(20 \cdot (-1)\).
Thus, we can write:
\[ -\sqrt{-20} = -\sqrt{20 \cdot (-1)} = -\sqrt{20} \cdot \sqrt{-1} \]
Knowing that \(\sqrt{-1} = i\), we can further simplify:
\[ -\sqrt{-20} = -\sqrt{20} \cdot i \]
Next, we can simplify \(\sqrt{20}\):
\[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \]
Substituting this back into our equation gives:
\[ -\sqrt{-20} = -2\sqrt{5} \cdot i \]
This can be expressed in standard form \(a + bi\) as:
\[ 0 - 2\sqrt{5} i \]
This corresponds to \(a = 0\) and \(b = -2\sqrt{5}\).
Now, looking for the correct response among the given options, we see that the correct result is:
\(-2\sqrt{5}i\)
So the correct response is:
negative 12 i Start Root 5 End Root (which is \(-2\sqrt{5} i\)).
1 answer