Home
Class 12
MATHS
If z^2+z+1=0 where z is a complex number...

If `z^2+z+1=0` where `z` is a complex number, then the value of `(z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2` is

A

54

B

6

C

12

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED|33 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED|65 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

If z is a complex number such that |z|>=2 then the minimum value of |z+(1)/(2)| is

For complex number z,|z-1|+|z+1|=2 then z lies on

Knowledge Check

  • For any two complex numbers z_(1),z_(2) the values of |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) , is

    A
    `|z_(1)|^(2)+|z_(2)|^(2)`
    B
    `2(|z_(1)|^(2)+|z_(2)|^(2))`
    C
    `(|z_(1)|+|z_(2)|)^(2)`
    D
    none of these

  • If z_1 and z_2 are two complex numbers such that z_1/z_2+z_2/z_1=1 , then

    A
    `z_1, z_2` are collinear
    B
    `z_1, z_2` and origin form a right angled triangle
    C
    `z_1, z_2` and the origin form an equilateral triangle
    D
    None of the above

  • If z_(1),z_(2) and z_(3) be unimodular complex numbers, then the maximum value of |z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2) , is

    A
    6
    B
    9
    C
    12
    D
    3

    • Similar Questions

    Explore conceptually related problems

    If Z_(1),Z_(2) are two non-zero complex numbers, then the maximum value of (Z_(1)bar(Z)_(2)+Z_(2)bar(Z)_(1))/(2|Z_(1)||Z_(2)|) is

    For complex numbers z_1 = 6+3i, z_2=3-I find (z_1)/(z_2)

    If z_(1) , z_(2), z_(3) be three unimodular complex numbers, then E = | z_(1) - z_(2) | ^(2) + | z_(2) - z_(3) | ^(2) + | z_(3) - z_(1)| ^(2) cannot exceed

    If z _(1) and z _(2) are two complex numbers such that (z _(1))/(z _(2)) + (z _(2))/(z _(1)) = 1, then

    Let z_1 and z_2 be complex numbers, then |z_1+z_2|^2+|z_1-z_2|^2 is equal to :

    Home
    Profile