Home
Class 11
MATHS
If z^2+z+1= 0 where z is a complex numbe...

If `z^2+z+1= 0` where z is a complex number, then the value of `(z+frac{1}{z})^2+(z^2+frac{1}{z^2})^2+(z^3+frac{1}{z^3})^2+…....+(z^6+frac{1}{z^6})^2` is

A

18

B

54

C

6

D

12

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

If z^2+z+1= 0 where z is a complex number, then the value of (z+frac{1}{z})^2+(z^2+frac{1}{z^2})^2+(z^3+frac{1}{z^3})^2 equals

If z is a complex number, then (bar(z^-1))(bar(z)) =

If z = r(costheta+isintheta) , then the value of frac{z}{barz}+frac{barz}{z} is

The complex number z satisfying the equation abs(frac{z-12}{z-8i})=frac{5}{3}, abs(frac{z-4}{z-8}) = 1

If z is a complex number such that frac{z-1}{z+1} is purely imaginary, then

If z_1 , z_2 and z_3 , z_4 are two pairs of conjugate complex numbers, then find arg( frac{z_1}{z_4} ) + arg( frac{z_2}{z_3} )

If z= frac{-2}{1+sqrt3i} , then the value of arg(z) is

If z_1 and z_2 are any complex numbers, then abs(z_1+z_2)^2+abs(z_1-z_2)^2 is equal to

If z_1, z_2, z_3 are complex numbers such that abs(z_1)= abs(z_2) = abs(z_3) = abs(frac{1}{z_1}+frac{1}{z_2}+frac{1}{z_3}) = 1 , then abs(z_1+z_2+z_3) is

If z = cos(frac{pi}{6})+isin(frac{pi}{6}) , then