Certainly! Let's solve this step-by-step.
1. Identify the scores: We need to clarify the scores given for Melissa and Tomas in the question.
- Melissa's score: [tex]\( 3 + 2i \)[/tex]
- Tomas's score: [tex]\( 8 - 6i \)[/tex]
2. Addition of complex numbers: To find the total score, we add the real parts and the imaginary parts separately.
- Real Parts:
- Melissa's real part: [tex]\( 3 \)[/tex]
- Tomas's real part: [tex]\( 8 \)[/tex]
- Sum of real parts: [tex]\( 3 + 8 = 11 \)[/tex]
- Imaginary Parts:
- Melissa's imaginary part: [tex]\( 2i \)[/tex]
- Tomas's imaginary part: [tex]\( -6i \)[/tex]
- Sum of imaginary parts: [tex]\( 2i + (-6i) = 2i - 6i = -4i \)[/tex]
3. Combine the sums: Combining the sum of the real parts and the sum of the imaginary parts, we get the total score:
[tex]\[
11 + (-4i) = 11 - 4i
\][/tex]
Therefore, Melissa and Tomas's total score is:
[tex]\[
\boxed{11 - 4i}
\][/tex]
