Complex number Inequalities

  • #1
kukumaluboy
61
1

Homework Statement



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The Attempt at a Solution


-1 < (z-w) /(1-z*w) < 1
[/B]
Hi can give clue. Im clueless
 

Answers and Replies

  • #2
36,096
13,013
-1 < (z-w) /(1-z*w) < 1
You cannot compare complex numbers with inequalities.

Hint: ##| \frac{a}{b} | = \frac{|a|}{|b|}##
 
  • #3
kukumaluboy
61
1
|z-w| < |1-z*w| ?? should i square both sides?
 
  • #4
36,096
13,013
I would simplify the problem a bit before.

How comfortable are you with substitutions?
I think this problem is solvable without, but it makes life easier if you can simplify it first.
 
  • #5
kukumaluboy
61
1
Honestly. we have never done these type of questions before. Our exams are always set with questions that we have nvr done before. This is a past year paper haha. Can teach me the one without the substitution ?
 
  • #6
36,096
13,013
Our exams are always set with questions that we have nvr done before.
Well, repeating equations you had before would be pointless, right?

You can write both z and w in terms of real and imaginary part, square both sides and see what you get. It gets much easier if you get rid of one of the four parameters before, however. You can multiply both sides by |z*/z|, that should work.

Edit: Forget the multiplication, it is not as complicated as I expected with the longer approach.
 
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