Mastering the Tricky Complex Numbers Proof: Tips and Tricks for Success!

In summary, the conversation discusses the equation |Z1 + Z2| ≤ |Z1| + |Z2| and how to approach solving it. The speaker shares their attempts at solving it and mentions using the triangle inequality to solve it geometrically. They also suggest writing the equation in the form of |z|^2 = z*z to simplify it.
  • #1
lektor
56
0
I recently was confronted by this monstrosity of a question in one of my mock exams.

|Z1 + Z2| ≤ |Z1| + |Z2|

I made a few attempts at it before becoming demoralized with the lack of progress..
|Z^2| was equal to Z1(conjugate)Z1
Hence equaling X^2 + Y^2

However even when expanding into x+iy form etc no avail, help is appreciated.
 
Physics news on Phys.org
  • #2
square both side and see if you notice anything and remember
if A=A then, surely A is less than or equal to A
 
Last edited:
  • #3
Geometrically this is just the triangle inequality. It just says that the sum of two sides of a triangle is always greater or equal than the third.

Since you know |z|^2=z*z. Why not write the left side out in this form?
ie: |z+w|^2=(z*+w*)(z+w)
 
  • #4
I'm sorry but I had to laugh when I read "I recently was confronted by this monstrosity of a question..." only to find the triangle inequality beneathe. lol.
 

What is the purpose of mastering complex number proofs?

The purpose of mastering complex number proofs is to develop a deeper understanding of the properties and operations of complex numbers, which are essential in many fields of science and mathematics.

What are some tips for approaching complex number proofs?

Some tips for approaching complex number proofs include breaking down the problem into smaller, more manageable steps, familiarizing yourself with common complex number identities and theorems, and practicing regularly to improve your problem-solving skills.

How can I improve my understanding of complex numbers?

To improve your understanding of complex numbers, it is important to review the basic concepts and properties, work through practice problems, and seek help from a tutor or teacher if needed. Additionally, exploring real-world applications of complex numbers can also enhance your understanding.

What are some common mistakes to avoid when working on complex number proofs?

Some common mistakes to avoid when working on complex number proofs include not fully understanding the problem, using incorrect properties or theorems, and making careless errors in calculations. It is also important to carefully check your work and identify any assumptions or logical flaws in your reasoning.

How can I become more confident in solving complex number proofs?

Becoming more confident in solving complex number proofs takes time and practice. It is important to start with simpler problems and gradually work your way up to more challenging ones. Seeking feedback from others and analyzing your mistakes can also help improve your confidence and problem-solving skills.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
7K
  • Precalculus Mathematics Homework Help
2
Replies
39
Views
4K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
11
Views
11K
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
Replies
1
Views
2K
  • Linear and Abstract Algebra
Replies
2
Views
6K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
10K
  • Precalculus Mathematics Homework Help
Replies
4
Views
3K
Back
Top