Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

SheldonEinstein

  • 2 years ago

Let z be a complex number than locus represented by |iz-1| + |z-i| = 2 is : a) a line , b) a circle , c) a pair of straight lines, d) a parabola

  • This Question is Closed
  1. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i think it is a l ine

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

    Sorry for the mistake in the question earlier , the modified quest. is in the post itself. I seek help from the users presented here as soon as possible,

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

    @satellite73 rethink please :)

  4. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    scratch that, i think it is a region bounded by two line

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

    OK so since it is IIT based so I will say : There may be no answers or multiple answers

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

    Well yes @satellite73 has the answer, it will be a line \(\textbf{segment}\)

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

    But I am half way stuck @satellite73 , can you show your work, I think @experimentX is also writing his work :)

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

    put z = x + iy you would get, \[ \sqrt{(y-1)^2 + x^2} + \sqrt{x^2 + (y-1)^2} = 2\] http://www.wolframalpha.com/input/?i=plot+\sqrt{%28y-1%29^2+%2B+x^2}+%2B+\sqrt{x^2+%2B+%28y-1%29^2}+%3D+2 guess it is a circle

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

    woops!! (y+1)^2

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

    What I can do is : \[\large{|(-iz-1)| + |(z-i)| =2}\] \[\large{|i(z+i)|+|z-i|=2}\] \[\large{|i||z+i| + |z-i| = 2 }\] \[\large{|z+i| + |z-i| = 2}\]

  11. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that looks good

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

    |dw:1352908224557:dw|

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

    So am I right in my way @experimentX @satellite73 ? (Since I am only given 54 seconds to do these type of questions so I prefer to use shortcuts that is here : not putting z = x + iy , my opinion said , yes ! x will be equal to zero if we are going to solve it! )

  14. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes \(x=0\)

  15. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i did it the donkey way but your way is much much better i think

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

    \(z=i\) is a solution

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

    Oh! No problem, sometimes we learn a lot from "that say donkey ways" , thanks for your time : @experimentX @satellite73

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

    |z| <= 1 and z = i

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

    no wonder it does not show in x's and y's

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

    \(z=-i\) is also a solution

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

    the solution is a line segment from +i to -i

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

    \[\large{|z+i| + |z-i| = 2}\] change of variables shift along the complex plane \[w=z+i\] \[{|w| + |w-2i| = 2}\]

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

    |dw:1352909335544:dw|

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

    circle + circle = circle?

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.