Question

Please help! Solve for x if 4+ix=2x+(y-x)i.
x=
a. 0
b. 1
c. 2
d. 4

Answer 1

Compex numbers, right?

Well every complex number is actually a combination of two different things, a real number and an imaginary number. So when two complex numbers equal each other, both their real and imaginary numbers must equal each other.\[\large \text{If}~~a+ib=c+id,~~\text{then}~~a=c~~~\text{and}~~~b=d\]So\[\large 4=2x~~\text{and}~~x=y-x\]But you only need one of these equations to solve it!

Do you understand now?

Answer 2

Oh o.k. Thanks! Is the answer 2? Just for confirmation?

Answer 3

yes

Answer 4

How would I find y?

Answer 5

@satellite73

Answer 6

Plug x into the second equation and solve. Answer in white letters below.

\[\color{white}{y=4}\]

Answer 7

Thank you!