Question

If (x + yi) + (2(x + yi) + 3i) = 9, what is x + yi?

A.
3 − i
B.
-3 + i
C.
-3 − i
D.
3 + i
E.
9 − 3i

Answer 1

Choice A is correct. x+yi = 3-i is the answer.

Explanation:

We have given an equation:

(x + yi) + (2(x + yi) + 3i) = 9

We have to find the value of x + yi =?

Solving the given equation we get,

(x + yi) + (2(x + yi) + 3i) = 9

(x + yi) + (2x+2yi+3i) = 9

x+yi +2x+2yi+3i =9

3x+3yi+3i = 9

3(x+yi+i) = 9

(x+yi+i) = 3

x+yi = 3-i is the answer.

Choice A is correct.

Answer 2

A.
`3-i`

Explanation:

Given the complex number expression;

`(x+yi)+(2(x+yi)+3i)=9`

Expand:

`(x+yi)+2(x+yi)+3i=9`

Group similar expressions;

`(x+yi)+2(x+yi)=9-3i`

Simplify

`3(x+yi)=9-3i`

Solve for
`(x+yi)`;

`3(x+yi)=3(3-i)`

Divide through by 3;

`(x+yi)=3-i`