Sure, let's analyze each of the given complex numbers and how they would be represented in the complex plane. A complex number is typically represented as [tex]\( a + bi \)[/tex], where [tex]\( a \)[/tex] is the real part and [tex]\( b \)[/tex] is the imaginary part.
1. First complex number: [tex]\( -3 + 8i \)[/tex]
- Real part (Re): [tex]\( -3 \)[/tex]
- Imaginary part (Im): [tex]\( 8 \)[/tex]
On the complex plane, this number is represented as the point [tex]\( (-3, 8) \)[/tex].
2. Second complex number: [tex]\( 4i \)[/tex]
- Real part (Re): [tex]\( 0 \)[/tex] (since there is no real component)
- Imaginary part (Im): [tex]\( 4 \)[/tex]
On the complex plane, this number is represented as the point [tex]\( (0, 4) \)[/tex].
3. Third complex number: [tex]\( 6 \)[/tex]
- Real part (Re): [tex]\( 6 \)[/tex]
- Imaginary part (Im): [tex]\( 0 \)[/tex] (since there is no imaginary component)
On the complex plane, this number is represented as the point [tex]\( (6, 0) \)[/tex].
4. Fourth complex number: [tex]\( 5 - 2i \)[/tex]
- Real part (Re): [tex]\( 5 \)[/tex]
- Imaginary part (Im): [tex]\( -2 \)[/tex]
On the complex plane, this number is represented as the point [tex]\( (5, -2) \)[/tex].
So, to summarize, we have extracted and plotted the following points in the complex plane:
- [tex]\( -3 + 8i \)[/tex] at [tex]\( (-3, 8) \)[/tex]
- [tex]\( 4i \)[/tex] at [tex]\( (0, 4) \)[/tex]
- [tex]\( 6 \)[/tex] at [tex]\( (6, 0) \)[/tex]
- [tex]\( 5 - 2i \)[/tex] at [tex]\( (5, -2) \)[/tex]
These points represent the positions of the given complex numbers in the complex plane.
