In exercise 23, find the real numbers x and y that make the equation true:
(5-2i)-7=x-(3+yi)

Question

In exercise 23, find the real numbers x and y that make the equation true:
(5-2i)-7=x-(3+yi)

anonymous · Answer

Regrouping things: 5-7+3-2i=x-iy--->x=5-7+3 and y=2

littlenugget · Answer

Can you explain again? sorry i got a little confused :3 @CarlosGP

anonymous · Answer

Sure. This is an equation that is using complex numbers,agree?

littlenugget · Answer

yep

anonymous · Answer

and you know that complex numbers have two parts: Real part and Imaginary part, agree?

littlenugget · Answer

yep

anonymous · Answer

How do you identify the imaginary part?

littlenugget · Answer

with i?

anonymous · Answer

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 · Answer

i think, so in this equation, which would be the imaginary part and which would be the rest?

anonymous · Answer

The imaginary part are all the terms multiplied by "i". Can you identify them?

littlenugget · Answer

2i, and yi

anonymous · Answer

Then the imaginary equation is -2i=-iy?

littlenugget · Answer

yep, i think?

anonymous · Answer

to be sure, delete in the given equation all the terms that are not multiplied by "i", dont you get: -2i=-iy

littlenugget · Answer

ohhhh now i see

anonymous · Answer

Then, that means y=2, isnt it true?

littlenugget · Answer

is it because you divide both sides by i?

anonymous · Answer

Exactly!
Now delete from the given equation all the terms multiplied by "i"

littlenugget · Answer

so it'd be 5-7=x-3

anonymous · Answer

Awesome! And what is the solution for the real part?  x=???

littlenugget · Answer

1

littlenugget · Answer

i mean -1

anonymous · Answer

Do it again, what is the solution of 5-7=x+3?

anonymous · Answer

sorry 5-7=x-3

littlenugget · Answer

-2=x-3
+3    +3
-----------
x=1

anonymous · Answer

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 · Answer

don't you?

littlenugget · Answer

so basically for one of these problems, i just do what you told me?

anonymous · Answer

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 · Answer

ohhhhhhhhhhhh that makes so much more sense now!!!!! THANK YOU SO MUCH!!!!!! :DDDD

anonymous · Answer

you are more than welcome! good luck!