Question

Express √-64 in terms of i:
√-64

Answer 1

To express \(\sqrt{-64}\) in terms of \(i\), we can rewrite it using the property of imaginary numbers.

First, we can separate the negative sign:

\[
\sqrt{-64} = \sqrt{64} \cdot \sqrt{-1}
\]

Since \(\sqrt{-1} = i\), we have:

\[
\sqrt{-64} = \sqrt{64} \cdot i
\]

Now, we calculate \(\sqrt{64}\):

\[
\sqrt{64} = 8
\]

Putting it all together gives:

\[
\sqrt{-64} = 8i
\]

Thus, \(\sqrt{-64} = 8i\).