Question

Can we multiply both sides of a complex equation with each of their conjugate equations, eg: if z+4=w+2
Can we write (z+4)(y+4)=(w+2)(u+2)
Where y and u are the conjugates of z and y respectively

Answer 1

You have to multiply both sides of the equation with the exact same thing. So if you multiply one side with its conjugate, you have to multiply the other side with that same conjugate. In effect, you would have to multiply both sides of the equation with both conjugates, which would kind of leave you in the same place.

Answer 2

true; so you'll have:

(z+4)(y+4) = (w+2)(y+4)

this way, both stil are equal.

Answer 3

Yeah.

Answer 4

did you get it iam? :)

Answer 5

Thank you for your reply sstarica. But can you provide me any mathematical proof for the same?
Does this thing have a name?

Answer 6

hmm,

Take this example

3 + 4 = 3 + 2 + 2

if I add another 2 in both sides I'll have

3+ 4+ 2 = 3 +2 + 2 +2
9 = 9

Sorry, I don't think I have a mathematical proof for this one, I can only provide you with a similar example.

Answer 7

does anybody have a mathematical proof for this one?

Answer 8

You all may be wondering, why I am so concerned about this thing. But there is a good reason. Many problems can be very easily solved using this result. I am providing some of them...............

Answer 9

why are you concerned? It's perfectly clear

if you want bot sides to be equal then you have to multiply,divide, add or subtract with the same number to keep them equal. You can google a mathematical proof :)

Answer 10

Q. The inequality |z-4|<|z-2| represents the region given by

1. Re(z)=0
2. Im (z)=0
Choose among 1 and 2

Answer 11

you want to find a number z that makes that expression true?

Answer 12

Let the conjugate of z be m
So we can write
|z-4||m-4|<|z-2||m-2|
Solving it we get Re(z)>3

Answer 13

Oh, I got you now, so? where's the problem?

Answer 14

I have a book before me, which is using this single (insignificant) result to solve problems, which would otherwise be extremely nonintuitive. Yet, I never know a book where I have seen this result listed among the group of other results.
This is why I posted this thing here, to see if people are unfamiliar with this thing like me

Answer 15

I don't like working with txtbooks. All books must have the same mathematical theorem!

Try googling it.

If not all books have the same mathematical theorem then that theorem you have is wrong.

Answer 16

Multiplying a complex number by its conjugate is the same taking its absolute value and squaring it. Since taking the absolute value of two sides of an equation leaves equality, and then squaring both sides also leaves equality, you can in fact preserve equality by multiplying both sides of the equation by their respective absolute values. check out the Wikipedia article on absolute values for a starting point: http://en.wikipedia.org/wiki/Absolute_value

Answer 17

Thanks a lot abhorsen

Answer 18

No problem.

Answer 19

Abhorsen, can you tell me how can I invite people to my study pad, as I did earlier in the older version of openstudy

Answer 20

I don't believe you can explicitly invite them, but you can send them the URL of the question you're asking and it'll direct them to the correct place.