Final answer:
Melissa and Tomas's combined total score in their game is calculated by adding their individual scores, 5 − 4i and 3 + 2i, which results in a total score of 8 − 2i.
Step-by-step explanation:
When combining the complex numbers of Melissa's score, 5 − 4i, and Tomas's score, 3 + 2i, we perform addition by combining the real parts and the imaginary parts separately. The real parts are 5 (from Melissa's score) and 3 (from Tomas's score) and the imaginary parts are − 4i (from Melissa's score) and +2i (from Tomas's score).
To find their total score, we add the real numbers and the imaginary numbers separately:
- Real parts: 5 + 3 = 8
- Imaginary parts: (− 4i) + (2i) = − 2i
Therefore, the total combined score is 8 − 2i.