Let a,b,x and y be real numbers such th...

Let a,b,x and y be real numbers such that a-b =1 and `y ne 0`. If the complex number `z = x +iy` satisfies `Im((az + b)/(z+1))=y` then which of the following is (are) possible value (s) of x?

`- 1 - sqrt(1 - y^(2))`

`1 + sqrt(1 + y^(2))`

`- 1 + sqrt(1 - y^(2))`

` 1 - sqrt(1 + y^(2))`

Text Solution

Verified by Experts

The correct Answer is:

A, C

Topper's Solved these Questions

COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
CIRCLES
VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the complex number z=x+i y satisfies I m((a z+b)/(z+1))=y , then which of the following is (are) possible value9s) of x?| -1-sqrt(1-y^2) (b) 1+sqrt(1+y^2) -1+sqrt(1-y^2) (d) -1-sqrt(1+y^2)

If x, y, z are positive real numbers such that x+y+z=a, then

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

For every real number age 0 , find all the complex numbers z that satisfy the equation 2|z|-4az+1+ ia =0

Let a, x, b in A.P, a, y, b in GP a, z, b in HP where a and b are disnict positive real numbers. If x = y + 2 and a = 5z , then which of the following is/are COR RECT ?

Let x, y, z be positive real numbers such that x + y + z = 12 and x^3y^4z^5 = (0.1)(600)^3 . Then x^3+y^3+z^3 is

A variable complex number z=x+iy is such that arg (z-1)/(z+1)= pi/2 . Show that x^2+y^2-1=0 .

If logy^(x)=(alog_(z)y)=(blog_(x)z=ab, then which of the following pairs of values for (a,b) is not possible ?

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 radius 1 (c)y-axis (d) none of these

If the complex numbers x and y satisfy x^3-y^3=98i and x-y=7i ,then x y=a+i b ,where a ,b , in Rdot The value of (a+b)//3 equals ______.

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE

The quadratic equation p(x)=0 with real coefficients has purely imagin...
Text Solution
|
For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...
Text Solution
|
Let a,b,x and y be real numbers such that a-b =1 and y ne 0. If the ...
Text Solution
|
If z(1)=p+iq and z(2) = u = iv are complex numbers such that |z(1)|=...
Text Solution
|
Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...
Text Solution
|
Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...
Text Solution
|
about to only mathematics
Text Solution
|
Find the centre and radius of the circle formed by all the points repr...
Text Solution
|
If one of the vertices of the square circumscribing the circle abs(z-1...
Text Solution
|
Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...
Text Solution
|
If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...
Text Solution
|
If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...
Text Solution
|
Express 1//(1-costheta+2isintheta) in the form x=i y .
Text Solution
|
If n is n odd integer that is greater than or equal to 3 but not a mul...
Text Solution
|
The real values of xa n dy for which the following equation is satisfi...
Text Solution
|
Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...
Text Solution
|
A relation R on set of complex numbers defined by Z(1)RZ(2) hArr (Z(1)...
Text Solution
|
Prove that the complex numbers z(1),z(2) and the origin form an equ...
Text Solution
|
If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...
Text Solution
|
Show that the area of the triangle on the Argand diagram formed by the...
Text Solution
|