Certainly! Let's solve the given problem step-by-step:
We are tasked with subtracting the complex number [tex]\(6 - 2j\)[/tex] from the complex number [tex]\(-2 + 6j\)[/tex].
1. Identify the given complex numbers:
[tex]\[
\text{First complex number} = -2 + 6j
\][/tex]
[tex]\[
\text{Second complex number} = 6 - 2j
\][/tex]
2. Perform the subtraction:
[tex]\[
(-2 + 6j) - (6 - 2j)
\][/tex]
3. Distribute the subtraction across the real and imaginary parts:
[tex]\[
= -2 + 6j - 6 + 2j
\][/tex]
4. Combine the real parts:
[tex]\[
-2 - 6 = -8
\][/tex]
5. Combine the imaginary parts:
[tex]\[
6j + 2j = 8j
\][/tex]
6. Combine the results from the previous steps:
[tex]\[
-8 + 8j
\][/tex]
Therefore, the result of subtracting the complex number [tex]\(6 - 2j\)[/tex] from [tex]\(-2 + 6j\)[/tex] is:
[tex]\[
\boxed{-8 + 8j}
\][/tex]
The real part of the result is [tex]\(-8\)[/tex], and the imaginary part is [tex]\(8\)[/tex]. So, summarizing:
[tex]\[
\text{Real part: } -8.0
\][/tex]
[tex]\[
\text{Imaginary part: } 8.0
\][/tex]
[tex]\[
\text{Resulting complex number: } -8 + 8j
\][/tex]
