# Math Help - Real numbers x and y

1. ## Real numbers x and y

Hello. I was hoping someone could help me with this problem:

Find the real numbers x and y that make the equation true.
-3 + yi = x + 6i

I was hoping that you guys could actually work it out so that I can try to figure out what you did. I want to learn how to do this not just get the answer. If it helps, I have been doing imaginary numbers and complex numbers. So it lies within that criteria I suppose.

Thank you so much for your help guys.

2. ## Re: Real numbers x and y

It's simpler than you think . . .

$\text{Find real numbers }x\text{ and }y\text{ that make the equation true.}$
. . $\text{-}3 + yi \:=\: x + 6i$

If two complex numbers are equal,
. . their real components are equal and their imaginary components are equal.

So we have: . $\begin{Bmatrix} \text{-}3 &=& x \\ y &=& 6\end{Bmatrix}$

Got it?

3. ## Re: Real numbers x and y

I think I see what you mean. So essentially, the answer is x=-3 and y=6. All because what is equal on one side would be equal on the other in terms of real numbers and imaginary components.

Wow, I feel like an idiot. :P That was pretty simple. Thank you so much!