Question

Evaluate the expression √-81 and write the result in the form a+bi
The real number a equals
The real number b equals

Answer 1

To evaluate the expression \( \sqrt{-81 \), we first note that the square root of a negative number can be expressed in terms of imaginary numbers.

We can rewrite \( -81 \) as follows:

\[
\sqrt{-81} = \sqrt{81 \cdot -1} = \sqrt{81} \cdot \sqrt{-1}
\]

We know that:

\[
\sqrt{81} = 9 \quad \text{and} \quad \sqrt{-1} = i
\]

Thus, substituting these values back in gives us:

\[
\sqrt{-81} = 9i
\]

In the form \( a + bi \), we can identify:

- The real number \( a = 0 \)
- The real number \( b = 9 \)

So, the final answers are:

- The real number \( a \) equals \( 0 \)
- The real number \( b \) equals \( 9 \)