Question

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

Answer 1

combine all your real parts on the left hand side
and
combine all your imaginary parts on the left hand side

Answer 2

can you try to do that @Mr.Man420 and show me what you get

Answer 3

just working with left hand side only

Answer 4

for now

Answer 5

for example
we can write 3x+yi+2(x+3yi)+4i
as 3x+yi+2x+6yi+4i
as 5x+i(y+6y+4)
as 5x+i(7y+4)
this is just an example of what I want you to do

Answer 6

And pretend we had my example=10
5x+i(7y+4)=10
and we wanted to find x and y such that this equation is true
well 5x=10 and 7y+4=0
we set our reals equal to our reals from both sides
and our imaginary equal to our imaginary from both sides
in my example 5x=10 gives x=2
and 7y+4=0 gives y=-4/7
so the x+yi satisfying my equation 5x+i(7y+4)=10 is 2-4i/7

Answer 7

Im not quite sure what you want me to do. you still have imaginary on both sides of your equation?

Answer 8

no 9 is real there is no i next to 9

Answer 9

ok.

Answer 10

I want you to collect your real parts on the left hand side
and then collect your imaginary parts on the left hand side
basically I'm trying to get you to write your left hand side in standard form of a complex number
that is write it in the form u+vi

Answer 11

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

First step distribute the 2 in front of the (x+yi)
x+yi+2x+2yi+3i
no you see all the things that have an i in it collect them together like I did in my example
and everything that doesn't have an i is real so collect those parts together