To determine which number among the given options is an example of a complex number that is not in the set of real numbers, we need to understand the nature of each number. Let's examine each option step-by-step:
1. Option [tex]\(-7\)[/tex]:
- This is a negative integer.
- It is a real number because it does not have an imaginary part.
2. Option [tex]\(2 + \sqrt{3}\)[/tex]:
- This is an expression involving a real number [tex]\(2\)[/tex] and a real square root [tex]\(\sqrt{3}\)[/tex].
- Both [tex]\(2\)[/tex] and [tex]\(\sqrt{3}\)[/tex] are real numbers, thus [tex]\(2 + \sqrt{3}\)[/tex] is also a real number.
3. Option [tex]\(4 + 9i\)[/tex]:
- This is of the form [tex]\(a + bi\)[/tex], where [tex]\(a = 4\)[/tex] and [tex]\(b = 9\)[/tex].
- Here, [tex]\(4\)[/tex] is a real part and [tex]\(9i\)[/tex] is an imaginary part (since [tex]\(i\)[/tex] is the imaginary unit).
- Because it has a non-zero imaginary part, [tex]\(4 + 9i\)[/tex] is a complex number.
4. Option [tex]\(\pi\)[/tex]:
- This is a famous mathematical constant representing the ratio of the circumference of a circle to its diameter.
- [tex]\(\pi\)[/tex] is known to be an irrational number and thus a real number.
Among the given options, all except [tex]\(4 + 9i\)[/tex] are real numbers. Therefore, the number that is a complex number and not in the set of real numbers is:
[tex]\[
\boxed{4 + 9i}
\][/tex]
