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]



Answer :

To find the combined score of Melissa and Tomas, we need to add their respective complex numbers.

Melissa's score is [tex]\( 5 - 4i \)[/tex].

Tomas's score is [tex]\( 3 + 2i \)[/tex].

To add complex numbers, we simply add their real parts and their imaginary parts separately:

1. Add the real parts:
- Melissa's real part: [tex]\( 5 \)[/tex]
- Tomas's real part: [tex]\( 3 \)[/tex]
- Sum of the real parts: [tex]\( 5 + 3 = 8 \)[/tex]

2. Add the imaginary parts:
- Melissa's imaginary part: [tex]\( -4i \)[/tex]
- Tomas's imaginary part: [tex]\( 2i \)[/tex]
- Sum of the imaginary parts: [tex]\( -4i + 2i = -2i \)[/tex]

So, combining the sums of the real parts and the imaginary parts, we get the total score:

[tex]\[ 8 - 2i \][/tex]

Thus, the correct total score of Melissa and Tomas is:

[tex]\[ \boxed{8 - 2i} \][/tex]