Certainly! Let's analyze each option one-by-one and write the complex numbers in the form [tex]\( a + bi \)[/tex], where [tex]\( a \)[/tex] is the real part and [tex]\( b \)[/tex] is the imaginary part.
1. [tex]\(-\frac{3}{2}\)[/tex]:
- This number is a purely real number with no imaginary part.
- In the form [tex]\( a + bi \)[/tex], this can be written as:
[tex]\[
-\frac{3}{2} + 0i
\][/tex]
Hence, [tex]\( a = -\frac{3}{2} \)[/tex] and [tex]\( b = 0 \)[/tex].
2. [tex]\(1 - i\)[/tex]:
- This number has both a real part and an imaginary part.
- The real part is 1, and the imaginary part is [tex]\(-1\)[/tex].
- In the form [tex]\( a + bi \)[/tex], this can be written as:
[tex]\[
1 - i
\][/tex]
Hence, [tex]\( a = 1 \)[/tex] and [tex]\( b = -1 \)[/tex].
3. [tex]\(\frac{3}{2} - i\)[/tex]:
- This number has both a real part and an imaginary part.
- The real part is [tex]\(\frac{3}{2}\)[/tex], and the imaginary part is [tex]\(-1\)[/tex].
- In the form [tex]\( a + bi \)[/tex], this can be written as:
[tex]\[
\frac{3}{2} - i
\][/tex]
Hence, [tex]\( a = \frac{3}{2} \)[/tex] and [tex]\( b = -1 \)[/tex].
4. [tex]\(\frac{5}{4} - \frac{5}{4}i\)[/tex]:
- This number has both a real part and an imaginary part.
- The real part is [tex]\(\frac{5}{4}\)[/tex], and the imaginary part is [tex]\(-\frac{5}{4}\)[/tex].
- In the form [tex]\( a + bi \)[/tex], this can be written as:
[tex]\[
\frac{5}{4} - \frac{5}{4}i
\][/tex]
Hence, [tex]\( a = \frac{5}{4} \)[/tex] and [tex]\( b = -\frac{5}{4} \)[/tex].
Thus, the complex numbers in the form [tex]\( a + bi \)[/tex] are:
[tex]\[
\begin{array}{l}
-\frac{3}{2} + 0i \\
1 - i \\
\frac{3}{2} - i \\
\frac{5}{4} - \frac{5}{4}i
\end{array}
\][/tex]
Or equivalently:
[tex]\[
\begin{aligned}
&-\frac{3}{2} + 0i, \\
&1 - i, \\
&\frac{3}{2} - i, \\
&\frac{5}{4} - \frac{5}{4}i.
\end{aligned}
\][/tex]
