Home
Class 11
MATHS
The complex number w...

The complex number which satisfies the condition `|(i+z)/(i-z)|=1\ ` lies on `c i r c l e\ x^2+y^2=1` b. `t h e\ x-a xi s` c. `t h e\ y-a xi s` d. `t h e\ l in e\ x+y=1`

A

Circle `x^(2) + y^(2) = 1`

B

the X-axis

C

the Y-axis

D

the line `x + y = 1`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that, `|(i+x)/(i-z)| = 1`
Let z = x + iy
`:. |(x + i(y+1))/(-x -i(y-1))| = 1 rArr (x^(2) + (y+1)^(2))/(x^(2) + (y-1)^(2)) =1`
`rArr x^(2) + (y+1)^(2)= x^(2)(y-1)^(2)`
`rArr 4y= 0 rArr y = 0`
So, z lies on X-axis (real axis).
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise TRUE/FALSE|9 Videos

  • BINOMIAL THEOREM

    NCERT EXEMPLAR|Exercise True/False|7 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos

Similar Questions

Explore conceptually related problems

The complex number which satisfies the condition |(i+z)/(i-z)|=1 lies on circle x^(2)+y^(2)=1 b.t the x-a xi s c. the y-a xi s d.the l in ex+y=1

If the complex number z=x+i y satisfies the condition |z+1|=1, then z lies on (a)x axis (b) circle with centre(-1,0) and radius1 (c)y-axis (d) none of these

y=x^(logx)"t h e n"dy / dx"i s" y=xlogy then dy/dx is

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot

Show that f(x)={(x-|x|)/(2),2 w h e nx!=0i sd i s con t inuou sa tx=0dotw h e nx=0

If x=5a n dy=-2t h e nx-2y=9. The contrapositive of this statement is A.If x-2y=9t h e nx=5a n dy=-2 B. If x-2y!=9t h e nx!=5a n dy!=-2 C. If x-2y!=9t h e nx!=5ory!=-2 D. If x-2y!=9t h e ne i t h e rx!=5a n dy!=-2

If [1 4 2 0]=[x y^2z0],y<0t h e nx-y+z= 5 (b) 2 (c) 1 (d) -3

If 5x^2-13 x y+6y^2=, t h e n x : y is 2:1 on l y b. 3:5 on l y c. 5:3 or 1:2 d. 3:5 or 2:1

Assuming full occupancy, a bogie of which class exhibits the highest profit margin? 3 t i e r b. A C-3 t i e r c. A C-t i e r d. A C-fi r s t c l a s s