Question

write in terms of i. simplify your answer as muc -√(-121)

Explanation:

Step1: Recall the definition of \(i\)

We know that \(i = \sqrt{-1}\), so we can rewrite the square root of a negative number as the square root of the positive number times \(i\). For \(\sqrt{-121}\), we can split it using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (where \(a = - 1\) and \(b = 121\)):
\(\sqrt{-121}=\sqrt{-1\times121}=\sqrt{-1}\times\sqrt{121}\)

Step2: Substitute \(i\) and simplify \(\sqrt{121}\)

Since \(\sqrt{-1}=i\) and \(\sqrt{121} = 11\) (because \(11\times11 = 121\)), we have \(\sqrt{-121}=i\times11 = 11i\). But our original expression is \(-\sqrt{-121}\), so we apply the negative sign:
\(-\sqrt{-121}=-11i\)

Answer:

\(-11i\)