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Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of [tex]$5-4i$[/tex] and Tomas has a score of [tex]$3+2i$[/tex], what is their total score?

A. [tex][tex]$8-6i$[/tex][/tex]
B. [tex]$8+6i$[/tex]
C. [tex]$8-2i$[/tex]
D. [tex][tex]$8+2i$[/tex][/tex]

Sagot :

GinnyAnswer
Let's break down the solution step-by-step to find the total score of Melissa and Tomas.

1. Identify the scores in the form of complex numbers:
- Melissa's score: [tex]\( 5 - 4i \)[/tex]
- Tomas's score: [tex]\( 3 + 2i \)[/tex]

2. Add the real parts of their scores:
- The real part of Melissa's score is [tex]\( 5 \)[/tex].
- The real part of Tomas's score is [tex]\( 3 \)[/tex].
- Real part of the total score: [tex]\( 5 + 3 = 8 \)[/tex].

3. Add the imaginary parts of their scores:
- The imaginary part of Melissa's score is [tex]\( -4i \)[/tex].
- The imaginary part of Tomas's score is [tex]\( 2i \)[/tex].
- Imaginary part of the total score: [tex]\( -4 + 2 = -2 \)[/tex].

4. Combine the real and imaginary parts to form the total score:
- The total score combines the real part [tex]\( 8 \)[/tex] and the imaginary part [tex]\( -2i \)[/tex].
- Hence, the total score is [tex]\( 8 - 2i \)[/tex].

Therefore, the combined score of Melissa and Tomas is [tex]\( 8 - 2i \)[/tex].

The correct answer is:
[tex]\[ \boxed{8 - 2i} \][/tex]
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