Home
Class 12
MATHS
z(1), z(3), and z(3) are complex numbers...

`z_(1), z_(3), and z_(3)` are complex numbers such that `z_(1) + z_(2) + z_(3)=0 and |z_(1)| = |z_(2)| = |z_(3)|` = 1 then `z_(1)^(2)+z_(2)^(2)+z_(3)^(3)`

A

3

B

2

C

1

D

0

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER -11 (UNSOLVED)

    FULL MARKS|Exercise PART-II|10 Videos

  • SAMPLE PAPER -11 (UNSOLVED)

    FULL MARKS|Exercise PART-III|10 Videos

  • SAMPLE PAPER -08 ( UNSOLVED)

    FULL MARKS|Exercise PART -IV|7 Videos

  • SAMPLE PAPER -12

    FULL MARKS|Exercise PART-I|1 Videos

Similar Questions

Explore conceptually related problems

a. Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=rgt0 and z_(1)+z_(2)+z_(3)!=0 . Prove that |(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))/(z_(1)+z_(2)+z_(3))|=r b. Find all cube roots of sqrt(3)+i .

If z_(1)" and "z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 then

If z_(1),z_(2), and z_(3) are three complex numbers such that |z_(1)| = 1, " " |z_(2)| = 2, " " |z_(3)| = 3 and |z_(1) + z_(2) + z_(3) | = 1, show that |9z_(1)z_(2) + 4 z_(1)z_(3) + z_(2)z_(3)| = 6 .

If z_(1)" and "z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0, Im(z_(1)z_(2))=0 then

Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1 then prove that |z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|

If z_(1),z_(2)andz_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|z_(1)+z_(2)+z_(3)|=1 , find the value of |1/z_(1)+1/z_(2)+1/z_(3)| .