If k>0, |z|=|w|=k, and alpha=(z-bar w)/(...

If `k>0`, `|z|=|w|=k`, and `alpha=(z-bar w)/(k^2+zbar(w))`, then `Re(alpha)` (A) 0 (B) `k/2` (C) `k` (D) None of these

`k//2`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise LEVEL - 1|90 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

If |z|=k and omega=(z-k)/(z+k) , then Re (omega) =

If plane 2x+3y+6z+k=0 is tangent to the sphere x^(2)+y^(2)+z^(2)+2x-2y+2z-6=0 , then a value of k is (a) 26 (b) 16 (c) -26 (d) none of these

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- bar w z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 (c) z=bar z (d) None of these

Four distinct points (k, 2k), (2, 0), (0, 2) and (0,0) lie on a circle for : (A) k = 0 (B) k = 6/5 (C) k = 1 (D) k = -1

In the relation y = r sin ( omega t - kx) , the dimensions of omega//k are

The centre of circle which passes through A (h, 0), B (0, k) and C (0, 0) is : (A) (h/2, 0) (B) (0, k/2) (C) (h/2, k/2) (D) (h, k)

If z is a complex number lying in the fourth quadrant of Argand plane and |[(kz)/(k+1)]+2i|>sqrt(2) for all real value of k(k!=-1), then range of "arg"(z) is (pi/8,0) b. (pi/6,0) c. (pi/4,0) d. none of these

Assume X, Y, Z, W and P are matrices of order 2 xxn , 3 xxk , 2 xxp , n xx3 and p xxk , respectively. Choose the correct answer The restriction on n, k and p so that P Y + W Y will be defined are:(A) k = 3, p = n (B) k is arbitrary, p=2 (C) p is arbitrary, k=3 (D) k=2 , p=3

For the solution of the gases W, X, Y and z in water at 298 K , the Henrys law constants ( K _ H ) are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is :

If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^2)),beta=2sin^(-1)((2x)/(1+x^2)) and tanpi/8=k , then (a) alpha+beta=pi for x in [(1,1)/k] (b) alpha+beta for x in (-k , k) (c) alpha+beta=pi for x in [(1,1)/k] (d) alpha+beta=0 for x in [-k , k]

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2

For a complex number z the minimum value of |z|+|z-cos alpha-i sin alp...
Text Solution
|
If 1,alpha(1),alpha(2),alpha(3),...,alpha(n-1) are n, nth roots of uni...
Text Solution
|
If k>0, |z|=|w|=k, and alpha=(z-bar w)/(k^2+zbar(w)), then Re(alpha) ...
Text Solution
|
If |z-1|=1, where z is a point on the argand plane, show that(z-2)/(z)...
Text Solution
|
Let 1, z(1),z(2),z(3),…., z(n-1) be the nth roots of unity. Then pro...
Text Solution
|
If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...
Text Solution
|
If for complex numbers z1 and z2 and |1-bar(z1)z2|^2-|z1-z2|^2=k(1-|z1...
Text Solution
|
If |a(i)|lt1lamda(i)ge0 for i=1,2,3,.......nandlamda(1)+lamda(2)+........
Text Solution
|
if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alp...
Text Solution
|
If sqrt(1-c^(2))=nc-1andz=e^(itheta)," then "(c)/(2n)(1+nz)(1+(n)/(z))...
Text Solution
|
If z=x+iy,x,y real , then |x|+|y|lek|z| where k is equal to :
Text Solution
|
If arg(z)=-pi/4 then the value of arg((z^5+(bar(z))^5)/(1+z(bar(z))))^...
Text Solution
|
If p/a + q/b + r/c=1 and a/p + b/q + c/r=0, then the value of p^(2)/a^...
Text Solution
|
If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...
Text Solution
|
Let |(barZ(1) - 2barz(2))//(2-z(1)barz(2))|= 1 and |z(2)| ne 1, where...
Text Solution
|
Let z be a complex number having the argument theta ,0 < theta < pi/2,...
Text Solution
|
If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...
Text Solution
|
If a, b are complex numbers and one of the roots of the equation x^(2)...
Text Solution
|
Solve for z : z^2-(3-2i)z=(5i-5)dot
Text Solution
|
Find number of values of complex numbers omega satisfying the system o...
Text Solution
|