A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

can u teach me, how i can solve this problem... Triangle inequality for complex numbers is |Z1 + Z2|<= |Z1| + |Z2| . Write down at least eight different conditions for which |Z1 + Z2|= |Z1| + |Z2| .

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let the angle between the two complex position be @ So the length of the Z1+Z2 complex point or in other words |Z1+Z2| is = \[\sqrt(Z _{1}^2\sin^2@+Z _{2}^2+Z _{1}^2\cos^2@+Z _{1}Z _{2}\cos@)\] Continued ........................

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let name that expression as A

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now when |Z1+Z2|=|Z1|+|Z2| Z1+Z2=A

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Squaring both sides and simplifying we get @=0

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So you can get the equation only when the amplitude of the complex number is the same. I hope you have understood Please note that here the symbol Z1 and Z2 is the magnitude of the actual Z1 and Z2

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got what u had explained...thank you so much...this open stdy really halp me to think out of the box..

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    As you asked on through chat how to calculate amplitude of a complex number, so here is the reply Lets take a complex number x+iy So its amplitude is y/x Lets take another example z=3+7i So its amplitude would be 7/3 According the reply I gave you, the equation |z1|+|z2|=|z1+z2| is valid only when the amplitude of two complex number is the same. So for an example The complex number z1= 2+i4 and the complex number z2=6+i12 holds the relationship |z1|+|z2|=|z1+z2| Hope, I have made myself clear

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So silly of me! All this time, I have been mentioning a wrong term. I am extremely sorry for that. Please note that in the above answer everywhere I have used the word ""amplitude"", it must be instead ""argument""

  9. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.