To simplify the expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] into the form [tex]\(a + bi\)[/tex], let's break it down step-by-step:
1. Calculate [tex]\(\sqrt{9}\)[/tex]:
[tex]\[
\sqrt{9} = 3
\][/tex]
2. Calculate [tex]\(\sqrt{-36}\)[/tex]:
The square root of a negative number involves an imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex]. Thus:
[tex]\[
\sqrt{-36} = \sqrt{36 \cdot (-1)} = \sqrt{36} \cdot \sqrt{-1} = 6i
\][/tex]
3. Add the two results together:
[tex]\[
\sqrt{9} + \sqrt{-36} = 3 + 6i
\][/tex]
Therefore, the expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] simplifies to:
[tex]\[
\boxed{3 + 6i}
\][/tex]
