Alright, let's plot each of the given complex numbers on the complex plane. The complex plane is a two-dimensional plane where the horizontal axis represents the real part and the vertical axis represents the imaginary part of a complex number.
Given complex numbers:
1. [tex]\(-3 + 8i\)[/tex]
2. [tex]\(4i\)[/tex]
3. [tex]\(6\)[/tex]
4. [tex]\(5 - 2i\)[/tex]
### Step-by-Step Solution:
1. For [tex]\(-3 + 8i\)[/tex]:
- The real part is [tex]\(-3\)[/tex].
- The imaginary part is [tex]\(8\)[/tex].
Therefore, the point [tex]\(-3 + 8i\)[/tex] is located at [tex]\((-3, 8)\)[/tex] on the complex plane.
[tex]\(-3 + 8i\)[/tex] is [tex]\((-3, 8)\)[/tex].
2. For [tex]\(4i\)[/tex]:
- The real part is [tex]\(0\)[/tex] (since there is no real number present, it is implicitly zero).
- The imaginary part is [tex]\(4\)[/tex].
Therefore, the point [tex]\(4i\)[/tex] is located at [tex]\((0, 4)\)[/tex] on the complex plane.
[tex]\(4i\)[/tex] is [tex]\((0, 4)\)[/tex].
3. For [tex]\(6\)[/tex]:
- The real part is [tex]\(6\)[/tex].
- The imaginary part is [tex]\(0\)[/tex] (since there is no imaginary component, it is implicitly zero).
Therefore, the point [tex]\(6\)[/tex] is located at [tex]\((6, 0)\)[/tex] on the complex plane.
[tex]\(6\)[/tex] is [tex]\((6, 0)\)[/tex].
4. For [tex]\(5 - 2i\)[/tex]:
- The real part is [tex]\(5\)[/tex].
- The imaginary part is [tex]\(-2\)[/tex].
Therefore, the point [tex]\(5 - 2i\)[/tex] is located at [tex]\((5, -2)\)[/tex] on the complex plane.
[tex]\(5 - 2i\)[/tex] is [tex]\((5, -2)\)[/tex].
### Summary:
- [tex]\(-3 + 8i\)[/tex] is [tex]\((-3, 8)\)[/tex]
- [tex]\(4i\)[/tex] is [tex]\((0, 4)\)[/tex]
- [tex]\(6\)[/tex] is [tex]\((6, 0)\)[/tex]
- [tex]\(5 - 2i\)[/tex] is [tex]\((5, -2)\)[/tex]
