Need to see if both complex numbers are positive or negative pls help

[obelisk1151]

so i need to find out if both numbers are positive or negative, this is it |z−w|/|z+ w|<1

 

[pka]

so i need to find out if both numbers are positive or negative, this is it |z−w|/|z+ w|<1

If you are asking if the complex numbers are signed numbers(\(\displaystyle \pm\)), then the answer is NO!
On the other hand if you asking for a solution for \(\displaystyle \dfrac{|z-w|}{|z+w|}<1\) where \(\displaystyle z~\&~w\) then you need to realize that absolute value is a real number.

 

[Deleted member 4993]

so i need to find out if both numbers are positive or negative, this is it |z−w|/|z+ w|<1

Please post the EXACT problem as it was presented to you. As posted, it does not make any sense to me!!

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment.

 

[obelisk1151]

If you are asking if the complex numbers are signed numbers(\(\displaystyle \pm\)), then the answer is NO!
On the other hand if you asking for a solution for \(\displaystyle \dfrac{|z-w|}{|z+w|}<1\) where \(\displaystyle z~\&~w\) then you need to realize that absolute value is a real number.

sorry its asking me if the real part of those complex numbers are either both positive or nagative

 

[obelisk1151]

Please post the EXACT problem as it was presented to you. As posted, it does not make any sense to me!!

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this assignment.

sorry its on german so i had to translate it but its asking if the real part of "z and w " are either positive or negative

 

[Deleted member 4993]

sorry its on german so i had to translate it but its asking if the real part of "z and w " are either positive or negative

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment.

 

[obelisk1151]

Show that: are the real parts of z, w∈C are both positive or both negative, then the inequality holds:

 

[Dr.Peterson]

so i need to find out if both numbers are positive or negative, this is it |z−w|/|z+ w|<1

sorry its on german so i had to translate it but its asking if the real part of "z and w " are either positive or negative

As I understand this, the question is

Given two complex numbers z and w such that |z−w|/|z+ w|<1, prove that the real parts of z and w are either both positive or both negative.​

It may be best if you show us the original question in German, so we can translate it for ourselves. Is this correct?

[EDITED to change my interpretation to one that may make sense.]

 

[obelisk1151]

As I understand this, the question is

Given that |z−w|/|z+ w|<1, can it be determined whether the real parts of z and w are positive or negative?​

It may be best if you show us the original question in German, so we can translate it for ourselves. As it stands, I don't think this has an answer (other than "no", to the question as I phrased it); that makes me think I still have it wrong.

Show that: if the real parts of z, w∈C are both positive or both negative, then the inequality holds:


ty in advance!

 

[obelisk1151]

As I understand this, the question is

Given two complex numbers z and w such that |z−w|/|z+ w|<1, can it be determined whether the real parts of z and w are positive or negative?​

It may be best if you show us the original question in German, so we can translate it for ourselves. As it stands, I don't think this has an answer (other than "no", to the question as I phrased it); that makes me think I still have it wrong.

you got it right"Given that |z−w|/|z+ w|<1, can it be determined whether the real parts of z and w are positive or negative?''

 

[Dr.Peterson]

Google translates this (correctly, I think) as

Show that if the real parts of z, w ∈ C are both positive or both negative, the inequality | z - w | / | z + w | <1 holds.​

This is almost the converse of what you originally said! (And it is not what I took it to be.)

One simple way to do this is to let z = a+bi and w = c+di, and simplify the expression | z - w | / | z + w |.

Another (based on what I was doing under the interpretation I had written, where the inequality was given) is to express the inequality as |z - w| < |z + w| and simplify it in terms of a, b, c, and d, and then try to show that that is true if ac > 0 (that is, if the signs of a and c are the same).

Please show your work on the problem, so we can help you with it.

 

[Deleted member 4993]

Show that: are the real parts of z, w∈C are both positive or both negative, then the inequality holds:View attachment 14661

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