Answer :
To express the given expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] in the form [tex]\(a + bi\)[/tex], follow these steps:
1. Calculate the Square Root of 9:
- The square root of 9 is straightforward since it's a positive number.
- [tex]\(\sqrt{9} = 3\)[/tex].
2. Calculate the Square Root of -36:
- Since [tex]\(-36\)[/tex] is a negative number, we'll involve imaginary numbers.
- [tex]\(\sqrt{-36}\)[/tex] can be expressed as [tex]\(\sqrt{36} \times \sqrt{-1}\)[/tex].
- The square root of 36 is [tex]\(6\)[/tex].
- The square root of [tex]\(-1\)[/tex] is denoted by the imaginary unit [tex]\(i\)[/tex].
- Therefore, [tex]\(\sqrt{-36} = 6i\)[/tex].
3. Combine the Results:
- Add the real part ([tex]\(3\)[/tex]) and the imaginary part ([tex]\(6i\)[/tex]) together.
- This gives us the expression in the form [tex]\(a + bi\)[/tex].
So, the expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] simplifies to [tex]\(3 + 6i\)[/tex].
1. Calculate the Square Root of 9:
- The square root of 9 is straightforward since it's a positive number.
- [tex]\(\sqrt{9} = 3\)[/tex].
2. Calculate the Square Root of -36:
- Since [tex]\(-36\)[/tex] is a negative number, we'll involve imaginary numbers.
- [tex]\(\sqrt{-36}\)[/tex] can be expressed as [tex]\(\sqrt{36} \times \sqrt{-1}\)[/tex].
- The square root of 36 is [tex]\(6\)[/tex].
- The square root of [tex]\(-1\)[/tex] is denoted by the imaginary unit [tex]\(i\)[/tex].
- Therefore, [tex]\(\sqrt{-36} = 6i\)[/tex].
3. Combine the Results:
- Add the real part ([tex]\(3\)[/tex]) and the imaginary part ([tex]\(6i\)[/tex]) together.
- This gives us the expression in the form [tex]\(a + bi\)[/tex].
So, the expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] simplifies to [tex]\(3 + 6i\)[/tex].
