Respuesta :

x + (7 - 3i) + (5 + 9i) + 13i = 10 - 5i

Subtract 13i from both sides

x + (7 -3i) + (5 + 9i) = 10 - 18i

Subtract (5 + 9i). MAKE SURE YOU SUBTRACT 9i TOO. In other words, distribute the negative and subtract 5 and 9i at the same time.

x + (7 - 3i) = 5 - 27i

Do the same with (7 - 3i). You'll be adding 3i since -(-3i) = 3i.

x = -2 - 24i

Answer:

the missing term is [tex](-2-24i)[/tex]

Step-by-step explanation:

Let

[tex](x+yi)[/tex]------> the missing term

we have

[tex](x+yi)+(7-3i)+(5+9i)+13i=10-5i[/tex]

Combine like terms in the left side

[tex](x+7+5)+(yi-3i+9i+13i)=10-5i[/tex]

[tex](x+12)+(yi+19i)=10-5i[/tex]

Solve the system of equations

[tex]x+12=10[/tex] ------> equation A

[tex]x=10-12=-2[/tex]

[tex]yi+19i=-5i[/tex] ------> equation B

[tex]yi=-5i-19i=-24i[/tex]

the missing term is [tex](-2-24i)[/tex]