Question

Find the missing term. () + (7 − 3i) + (5 + 9i) + 13i = 10 − 5i.

Answer 1

the missing term is
`(-2-24i)`

Explanation:

Let

`(x+yi)`------> the missing term

we have

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

Combine like terms in the left side

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

`(x+12)+(yi+19i)=10-5i`

Solve the system of equations

`x+12=10` ------> equation A

`x=10-12=-2`

`yi+19i=-5i` ------> equation B

`yi=-5i-19i=-24i`

the missing term is
`(-2-24i)`

Answer 2

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