littlenugget
  • littlenugget
In exercise 23, find the real numbers x and y that make the equation true: (5-2i)-7=x-(3+yi)
Precalculus
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Regrouping things: 5-7+3-2i=x-iy--->x=5-7+3 and y=2
littlenugget
  • littlenugget
Can you explain again? sorry i got a little confused :3 @CarlosGP
anonymous
  • anonymous
Sure. This is an equation that is using complex numbers,agree?

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littlenugget
  • littlenugget
yep
anonymous
  • anonymous
and you know that complex numbers have two parts: Real part and Imaginary part, agree?
littlenugget
  • littlenugget
yep
anonymous
  • anonymous
How do you identify the imaginary part?
littlenugget
  • littlenugget
with i?
anonymous
  • anonymous
Correct! Then they are in fact giving you two equations: One for the imaginary part (all the terms multiplied by i) and another for the rest (the real part). Does it make sense to you?
littlenugget
  • littlenugget
i think, so in this equation, which would be the imaginary part and which would be the rest?
anonymous
  • anonymous
The imaginary part are all the terms multiplied by "i". Can you identify them?
littlenugget
  • littlenugget
2i, and yi
anonymous
  • anonymous
Then the imaginary equation is -2i=-iy?
littlenugget
  • littlenugget
yep, i think?
anonymous
  • anonymous
to be sure, delete in the given equation all the terms that are not multiplied by "i", dont you get: -2i=-iy
littlenugget
  • littlenugget
ohhhh now i see
anonymous
  • anonymous
Then, that means y=2, isnt it true?
littlenugget
  • littlenugget
is it because you divide both sides by i?
anonymous
  • anonymous
Exactly! Now delete from the given equation all the terms multiplied by "i"
littlenugget
  • littlenugget
so it'd be 5-7=x-3
anonymous
  • anonymous
Awesome! And what is the solution for the real part? x=???
littlenugget
  • littlenugget
1
littlenugget
  • littlenugget
i mean -1
anonymous
  • anonymous
Do it again, what is the solution of 5-7=x+3?
anonymous
  • anonymous
sorry 5-7=x-3
littlenugget
  • littlenugget
-2=x-3 +3 +3 ----------- x=1
anonymous
  • anonymous
x=1, exactly! Have you got the rationale? Whenever you have an equation with complex numbers, obtain two equations, one for the real part and another for the imaginary part. And you know how to identify them already!
anonymous
  • anonymous
don't you?
littlenugget
  • littlenugget
so basically for one of these problems, i just do what you told me?
anonymous
  • anonymous
yes. Obtain the real part equation eliminating in the given equation all the terms multiplied by "i" and solve. And eliminate all the terms not multiplied by "i" in the given equation and solve.
littlenugget
  • littlenugget
ohhhhhhhhhhhh that makes so much more sense now!!!!! THANK YOU SO MUCH!!!!!! :DDDD
anonymous
  • anonymous
you are more than welcome! good luck!

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