Question

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

Answer 1

i think it is a l ine

Answer 2

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,

Answer 3

@satellite73 rethink please :)

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

woops!! (y+1)^2

Answer 10

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

Answer 11

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

Answer 12

that looks good