anonymous
  • anonymous
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
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
i think it is a l ine
anonymous
  • anonymous
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,
anonymous
  • anonymous
@satellite73 rethink please :)

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anonymous
  • anonymous
scratch that, i think it is a region bounded by two line
anonymous
  • anonymous
OK so since it is IIT based so I will say : There may be no answers or multiple answers
anonymous
  • anonymous
Well yes @satellite73 has the answer, it will be a line \(\textbf{segment}\)
anonymous
  • anonymous
But I am half way stuck @satellite73 , can you show your work, I think @experimentX is also writing his work :)
experimentX
  • experimentX
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
experimentX
  • experimentX
woops!! (y+1)^2
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=plot+%7C+sqrt%28%28y%2B1%29%5E2%2Bx%5E2%29%2Bsqrt%28x%5E2%2B%28y-1%29%5E2%29+%3D+2
anonymous
  • anonymous
What I can do is : \[\large{|(-iz-1)| + |(z-i)| =2}\] \[\large{|i(z+i)|+|z-i|=2}\] \[\large{|i||z+i| + |z-i| = 2 }\] \[\large{|z+i| + |z-i| = 2}\]
anonymous
  • anonymous
that looks good
anonymous
  • anonymous
|dw:1352908224557:dw|
anonymous
  • anonymous
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! )
anonymous
  • anonymous
yes \(x=0\)
anonymous
  • anonymous
i did it the donkey way but your way is much much better i think
UnkleRhaukus
  • UnkleRhaukus
\(z=i\) is a solution
anonymous
  • anonymous
Oh! No problem, sometimes we learn a lot from "that say donkey ways" , thanks for your time : @experimentX @satellite73
experimentX
  • experimentX
|z| <= 1 and z = i
experimentX
  • experimentX
no wonder it does not show in x's and y's
UnkleRhaukus
  • UnkleRhaukus
\(z=-i\) is also a solution
experimentX
  • experimentX
the solution is a line segment from +i to -i
UnkleRhaukus
  • UnkleRhaukus
\[\large{|z+i| + |z-i| = 2}\] change of variables shift along the complex plane \[w=z+i\] \[{|w| + |w-2i| = 2}\]
UnkleRhaukus
  • UnkleRhaukus
|dw:1352909335544:dw|
UnkleRhaukus
  • UnkleRhaukus
circle + circle = circle?

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