Home
Class 12
MATHS
If z(1),z(2),z(3) andz(4) are the roots ...

If `z_(1),z_(2),z_(3) andz_(4)` are the roots of the equation `z^(4)=1,` the value of`sum_(i=1)^(4)z_i^(3)`is

A

0

B

1

C

`i,i=sqrt(-1)`

D

`1+i,i=sqrt(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise For Session 3|15 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

The solution of the equation |z|-z=1+2i is :

If z_(1),z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, the find the value of arg(z_(1)/z_(4)) + arg(z_(2)//z_(3)) .

z_(1) and z_(2) are the roots of the equation z^(2) -az + b=0 where |z_(1)|=|z_(2)|=1 and a,b are nonzero complex numbers, then

Complex numbers z_(1),z_(2),z_(3) are the vertices of A,B,C respectively of an equilteral triangle. Show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

Find all the roots of the equation : (3z -1)^4+(z-2)^4 =0 in the simplified form of a + ib.

If |z_(1) -1|le,|z_(2) -2| le2,|z_(3) - 3|le 3, then find the greatest value of |z_(1) + z_(2) + z_(3)|

If z_(1),z_(2)inC,z_(1)^(2)+z_(2)^(2)inR,z_(1)(z_(1)^(2)-3z_(2)^(2))=2 and z_(2)(3z_(1)^(2)-z_(2)^(2))=11, the value of z_(1)^(2)+z_(2)^(2) is

Consider four complex numbers z_(1)=2+2i, , z_(2)=2-2i,z_(3)=-2-2iandz_(4)=-2+2i),where i=sqrt(-1), Statement - 1 z_(1),z_(2),z_(3)andz_(4) constitute the vertices of a square on the complex plane because Statement - 2 The non-zero complex numbers z,barz, -z,-barz always constitute the vertices of a square.

If z_(1),z_(2)andz_(3) are the vertices of an equilasteral triangle with z_(0) as its circumcentre , then changing origin to z^(0) ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.