Answer :
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]
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]
