Very clever complex inequality.

Thread starter mathwizarddud
Start date Jun 28, 2008
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Complex Inequality

In summary, a "very clever complex inequality" is a mathematical statement involving complex numbers that requires creative or non-traditional methods to solve or prove. It differs from a regular inequality in that it involves complex numbers and often requires more unconventional thinking. Examples of "very clever complex inequalities" include the Cauchy-Schwarz inequality and the Minkowski inequality, which are commonly used in various fields of science. These types of inequalities are important in science because they can provide new insights and solutions to complex problems. To solve a "very clever complex inequality," one must think outside the box and have a strong understanding of complex numbers, while also being open to trying different approaches and techniques.

Jun 28, 2008

mathwizarddud

Prove that for every complex number z it happens that:

[tex]|z+10|+|z+11|+|z+19| \le |z+8|+|z+12|+|z+20|[/tex]

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Jun 28, 2008

alyscia

let z = a+ bi and physically evaluate the modulus.

Is this some homework question? I am not sure why this is in the analysis section.

Related to Very clever complex inequality.

1. What is a "very clever complex inequality"?

A "very clever complex inequality" refers to a mathematical statement that involves complex numbers and utilizes creative or non-traditional methods to solve or prove the inequality.

2. How is a "very clever complex inequality" different from a regular inequality?

A "very clever complex inequality" is different from a regular inequality in that it involves complex numbers, which are numbers that have both a real and imaginary component. It also often requires more creative or out-of-the-box thinking to solve or prove.

3. What are some examples of "very clever complex inequalities"?

One famous example is the "Cauchy-Schwarz inequality," which states that for any two vectors, the dot product of the two vectors is less than or equal to the product of their magnitudes. Another example is the "Minkowski inequality," which is a generalization of the triangle inequality for vectors in a Euclidean space.

4. Why are "very clever complex inequalities" important in science?

Complex numbers and inequalities are often used in various fields of science, such as physics, engineering, and economics. "Very clever complex inequalities" can provide new insights and solutions to complex problems in these fields, making them an important tool for scientists.

5. How can one approach solving a "very clever complex inequality"?

Solving a "very clever complex inequality" often requires thinking outside the box and utilizing creative methods. It is important to have a strong understanding of complex numbers and how they work, as well as being open to trying different approaches and techniques in order to find the solution.