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

Question

anonymous · Answer

3 − i
-3 + i
-3 − i
3 + i
9 − 3i

aum · Answer

On the left hand side, group the real terms together and the imaginary terms together first.  What do you get?

anonymous · Answer

What should it look like

aum · Answer

(x + yi) + (2(x + yi) + 3i) = 9
x + yi + 2x + 2yi + 3i = 9
x + 2x + (yi + 2yi + 3i) = 9
3x + (3yi + 3i) = 9
3x + (y + 3)*3i = 9

3x = 9  and  y + 3 = 0
x = 3  and  y = -3
x + yi = 3 - 3i

aum · Answer

None of the answers match.  Can you post a link to the original question?

anonymous · Answer

attachment

aum · Answer

Hang on.  I found my mistake:
(x + yi) + (2(x + yi) + 3i) = 9 
x + yi + 2x + 2yi + 3i = 9 
x + 2x + (yi + 2yi + 3i) = 9 
3x + (3yi + 3i) = 9 
3x + (y + 1)*3i = 9   (mistake in this line earlier).
3x = 9 and y + 1 = 0 
x = 3 and y = -1 
x + yi = 3 - i

anonymous · Answer

Thank you!