Let's analyze the complex number [tex]\(7 - \sqrt{3} i\)[/tex] and verify each statement.
1. 7 is the real part of the number.
In a complex number, the real part is the number without the imaginary unit [tex]\(i\)[/tex]. Here, [tex]\(7\)[/tex] is the real part of [tex]\(7 - \sqrt{3} i\)[/tex].
The statement is true.
2. [tex]\(\sqrt{3}\)[/tex] is the imaginary part of the number.
For a complex number [tex]\(a + bi\)[/tex], the imaginary part is the coefficient of the imaginary unit [tex]\(i\)[/tex]. In this case, the coefficient of [tex]\(i\)[/tex] is [tex]\(-\sqrt{3}\)[/tex], not [tex]\(\sqrt{3}\)[/tex].
The statement is false.
3. [tex]\(7 - \sqrt{3}\)[/tex] is the coefficient of [tex]\(i\)[/tex].
The coefficient of [tex]\(i\)[/tex] in the complex number [tex]\(7 - \sqrt{3} i\)[/tex] is [tex]\(-\sqrt{3}\)[/tex], not [tex]\(7 - \sqrt{3}\)[/tex].
The statement is false.
4. This number is the sum of a real number and an imaginary number.
A complex number [tex]\(a + bi\)[/tex] is the sum of its real part [tex]\(a\)[/tex] and its imaginary part [tex]\(bi\)[/tex]. Here, [tex]\(7 - \sqrt{3} i\)[/tex] is indeed the sum of the real number [tex]\(7\)[/tex] and the imaginary number [tex]\(-\sqrt{3} i\)[/tex].
The statement is true.
So, the true statements are:
- 7 is the real part of the number.
- This number is the sum of a real number and an imaginary number.
