Certainly! Let's analyze and break down the expression:
We start with the expression:
[tex]\[ 3 - \sqrt{3}i \][/tex]
### Step-by-Step Solution
1. Identify the Real and Imaginary Parts:
- The given expression is in the form of a complex number, where a complex number can be written as [tex]\( a + bi \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are real numbers, and [tex]\( i \)[/tex] is the imaginary unit with the property that [tex]\( i^2 = -1 \)[/tex].
2. Extract the Real Part:
- In the expression [tex]\( 3 - \sqrt{3}i \)[/tex], the real part of the complex number is the term without [tex]\( i \)[/tex].
- Therefore, the real part is [tex]\( \boxed{3.0} \)[/tex].
3. Extract the Imaginary Part:
- The imaginary part of the complex number is the coefficient of [tex]\( i \)[/tex].
- In this case, that coefficient is [tex]\( -\sqrt{3} \)[/tex].
- Evaluating [tex]\( \sqrt{3} \)[/tex] gives us approximately [tex]\( 1.7320508075688772 \)[/tex]. Since the coefficient of [tex]\( i \)[/tex] is negative, the imaginary part is [tex]\( -1.7320508075688772 \)[/tex].
- Therefore, the imaginary part is [tex]\( \boxed{-1.7320508075688772} \)[/tex].
### Conclusion
By identifying the real part and the imaginary part of the complex number [tex]\( 3 - \sqrt{3}i \)[/tex], we can conclude that:
- The real part is [tex]\( 3.0 \)[/tex].
- The imaginary part is [tex]\( -1.7320508075688772 \)[/tex].
So, the complex number [tex]\( 3 - \sqrt{3}i \)[/tex] has the real part [tex]\( 3.0 \)[/tex] and the imaginary part [tex]\( -1.7320508075688772 \)[/tex].
