- #1
kukumaluboy
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Homework Statement
The Attempt at a Solution
-1 < (z-w) /(1-z*w) < 1
[/B]
Hi can give clue. I am clueless
Solving Complex Number Inequalities
- Thread starter kukumaluboy
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In summary, the problem is to find the range of values for the complex number (z-w) / (1-z*w), with the given condition that it must be between -1 and 1. The conversation discusses different approaches to solving this problem, including using substitutions and simplifying the problem before squaring both sides. Ultimately, it is suggested to write z and w in terms of their real and imaginary parts and then square both sides to find the solution.
-1 < (z-w) /(1-z*w) < 1
[/B]
Hi can give clue. I am clueless
- #2
mfb
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You cannot compare complex numbers with inequalities.kukumaluboy said:
Hint: ##| \frac{a}{b} | = \frac{|a|}{|b|}##
- #3
kukumaluboy
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|z-w| < |1-z*w| ?? should i square both sides?
- #4
mfb
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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.
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
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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
mfb
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Well, repeating equations you had before would be pointless, right?kukumaluboy said:
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.
Last edited:
FAQ: Solving Complex Number Inequalities
What are complex number inequalities?
Complex number inequalities are equations that involve complex numbers and use the symbols >, <, ≥, and ≤ to compare two complex numbers.
How do you solve complex number inequalities?
To solve complex number inequalities, you must first isolate the real and imaginary parts of the complex numbers on one side of the inequality sign. Then, you can compare the real numbers and the imaginary numbers separately to determine the solution set.
What are some common properties of complex number inequalities?
Some common properties of complex number inequalities include the addition and multiplication properties, which state that if a > b and c > d, then a + c > b + d and ac > bd.
Can complex number inequalities have multiple solutions?
Yes, complex number inequalities can have multiple solutions. This is because complex numbers have both a real and imaginary part, so there can be multiple combinations of these parts that satisfy the inequality.
How can complex number inequalities be applied in real life?
Complex number inequalities can be applied in various fields such as engineering, physics, and economics. For example, in electrical engineering, complex number inequalities can be used to analyze alternating current circuits and determine the stability of a system.