To find the difference between the complex numbers [tex]\(7 + 3i\)[/tex] and [tex]\(3 - 7i\)[/tex], we subtract the second complex number from the first.
Let's break down the process step by step:
1. Write down the complex numbers:
[tex]\[
z_1 = 7 + 3i \quad \text{and} \quad z_2 = 3 - 7i
\][/tex]
2. Set up the subtraction:
[tex]\[
(7 + 3i) - (3 - 7i)
\][/tex]
3. Distribute the negative sign across [tex]\( (3 - 7i) \)[/tex]:
[tex]\[
7 + 3i - 3 + 7i
\][/tex]
4. Combine the real parts and the imaginary parts separately:
- Real parts: [tex]\(7 - 3 = 4\)[/tex]
- Imaginary parts: [tex]\(3i + 7i = 10i\)[/tex]
5. Combine the results:
[tex]\[
4 + 10i
\][/tex]
So, the difference between the complex numbers [tex]\(7 + 3i\)[/tex] and [tex]\(3 - 7i\)[/tex] is [tex]\(4 + 10i\)[/tex].
Therefore, the correct answer is:
A. [tex]\(4 + 10i\)[/tex]
