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Math Help - Real numbers x and y

  1. #1
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    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.
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  2. #2
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    Re: Real numbers x and y

    Hello, DreadfulGlory!

    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?
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  3. #3
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    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!
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