Home
Class 12
MATHS
Let omega be the complex number cos((2...

Let `omega` be the complex number `cos((2pi)/3)+isin((2pi)/3)`. Then the number of distinct complex cos numbers z satisfying `Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0` is

Text Solution

Verified by Experts

The correct Answer is:
1
Let `A=[(1" "omega" "omega^2),(omega" "omega^2" "1),(omega^2" " 1 " "z+omega)]`
`A=[(0" "0" "0),(0" "0" "0),(0" "0" "0)]`and Tr (A)=0,|A|=0
`A^3=0`
`A=[(z+1" "omega" "omega^3),(omega" "z+omega^2" "1),(omega^2" "1" "z+omega)]`=[A+zl]=0
`rArr " "z^3=0`
`rArr z=0 ` the number of z satisfying the given equation is 1.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 DE-MOIVRES THEOREM,CUBE ROOTS AND nth ROOTS OF UNITY ( TRUE/FLASE)|1 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 DE-MOIVRES THEOREM,CUBE ROOTS AND nth ROOTS OF UNITY ( ANALYTICAL & DESCRIPTIVE QUESTIONS)|4 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 5 DE-MOIVRES THEOREM,CUBE ROOTS AND nth ROOTS OF UNITY ( MATCH THE COLUMNS )|1 Videos

  • CIRCLE

    IIT JEE PREVIOUS YEAR|Exercise Topic 5 Integer Answer type Question|1 Videos

  • DEFINITE INTEGRATION

    IIT JEE PREVIOUS YEAR|Exercise LIMITS AS THE SUM|6 Videos