If the roots of (z-1)^n=i(z+1)^n are plo...

If the roots of `(z-1)^n=i(z+1)^n` are plotted in ten Arg and plane, then prove that they are collinear.

on a parabola

concyclic

collinear

the vertices of a

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

, a point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

if omega is the nth root of unity and Z_1 , Z_2 are any two complex numbers , then prove that . Sigma_(k=0)^(n-1)| z_1+ omega^k z_2|^2=n{|z_1|^2+|z_2|^2} where n in N

If n >1 , show that the roots of the equation z^n=(z+1)^n are collinear.

Show that the roots of equation (1+z)^n=(1-z)^n are -i tan (rpi/n), r=0,1,2,,…………,(n-1) excluding the vlaue when n is even and r=n/2

Find the locus of z if arg ((z-1)/(z+1))= pi/4

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 w h e r e lambda in R-{0}, then prove that points corresponding to z_1, z_2a n dz_3 are collinear .

Statement-1: If z_(1),z_(2) are affixes of two fixed points A and B in the Argand plane and P(z) is a variable point such that "arg" (z-z_(1))/(z-z_(2))=pi/2 , then the locus of z is a circle having z_(1) and z_(2) as the end-points of a diameter. Statement-2 : arg (z_(2)-z_(1))/(z_(1)-z) = angleAPB

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

If n in N >1 , then the sum of real part of roots of z^n=(z+1)^n is equal to

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2

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
|
For |z-1|=1, show that tan{[a r g(z-1)]//2}-(2i//z)=-idot
Text Solution
|
If nge3and1,alpha(1),alpha(2),.......,alpha(n-1) are nth roots of unit...
Text Solution
|
Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...
Text Solution
|